Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them
Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie s...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Salgado, G. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2003 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2003 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 241(2003), 2-3 vom: 19. Sept., Seite 505-518 |
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| Übergeordnetes Werk: |
volume:241 ; year:2003 ; number:2-3 ; day:19 ; month:09 ; pages:505-518 |
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| DOI / URN: |
10.1007/s00220-003-0930-5 |
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| Katalog-ID: |
SPR002330369 |
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| 100 | 1 | |a Salgado, G. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Lie Superalgebras Based on $ _{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
| 264 | 1 | |c 2003 | |
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| 520 | |a Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ _{n} $ and whose odd module is $ _{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ _{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ _{2} $. | ||
| 650 | 4 | |a Equivalence Class |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Complex Number |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Automorphism Group |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Geometric Structure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Isomorphism Class |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Sánchez-Valenzuela, O.A. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Communications in mathematical physics |d Berlin : Springer, 1965 |g 241(2003), 2-3 vom: 19. Sept., Seite 505-518 |w (DE-627)253721628 |w (DE-600)1458931-X |x 1432-0916 |7 nnns |
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10.1007/s00220-003-0930-5 doi (DE-627)SPR002330369 (SPR)s00220-003-0930-5-e DE-627 ger DE-627 rakwb eng Salgado, G. verfasserin aut Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 Sánchez-Valenzuela, O.A. aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 241(2003), 2-3 vom: 19. Sept., Seite 505-518 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:241 year:2003 number:2-3 day:19 month:09 pages:505-518 https://dx.doi.org/10.1007/s00220-003-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 241 2003 2-3 19 09 505-518 |
| spelling |
10.1007/s00220-003-0930-5 doi (DE-627)SPR002330369 (SPR)s00220-003-0930-5-e DE-627 ger DE-627 rakwb eng Salgado, G. verfasserin aut Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 Sánchez-Valenzuela, O.A. aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 241(2003), 2-3 vom: 19. Sept., Seite 505-518 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:241 year:2003 number:2-3 day:19 month:09 pages:505-518 https://dx.doi.org/10.1007/s00220-003-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 241 2003 2-3 19 09 505-518 |
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10.1007/s00220-003-0930-5 doi (DE-627)SPR002330369 (SPR)s00220-003-0930-5-e DE-627 ger DE-627 rakwb eng Salgado, G. verfasserin aut Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 Sánchez-Valenzuela, O.A. aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 241(2003), 2-3 vom: 19. Sept., Seite 505-518 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:241 year:2003 number:2-3 day:19 month:09 pages:505-518 https://dx.doi.org/10.1007/s00220-003-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 241 2003 2-3 19 09 505-518 |
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10.1007/s00220-003-0930-5 doi (DE-627)SPR002330369 (SPR)s00220-003-0930-5-e DE-627 ger DE-627 rakwb eng Salgado, G. verfasserin aut Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 Sánchez-Valenzuela, O.A. aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 241(2003), 2-3 vom: 19. Sept., Seite 505-518 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:241 year:2003 number:2-3 day:19 month:09 pages:505-518 https://dx.doi.org/10.1007/s00220-003-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 241 2003 2-3 19 09 505-518 |
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10.1007/s00220-003-0930-5 doi (DE-627)SPR002330369 (SPR)s00220-003-0930-5-e DE-627 ger DE-627 rakwb eng Salgado, G. verfasserin aut Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 Sánchez-Valenzuela, O.A. aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 241(2003), 2-3 vom: 19. Sept., Seite 505-518 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:241 year:2003 number:2-3 day:19 month:09 pages:505-518 https://dx.doi.org/10.1007/s00220-003-0930-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 241 2003 2-3 19 09 505-518 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR002330369</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327161630.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2003 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-003-0930-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR002330369</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00220-003-0930-5-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Salgado, G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2003</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2003</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equivalence Class</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex Number</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Automorphism Group</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric Structure</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Isomorphism Class</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sánchez-Valenzuela, O.A.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Communications in mathematical physics</subfield><subfield code="d">Berlin : Springer, 1965</subfield><subfield code="g">241(2003), 2-3 vom: 19. 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Salgado, G. |
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Salgado, G. misc Equivalence Class misc Complex Number misc Automorphism Group misc Geometric Structure misc Isomorphism Class Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
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Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them Equivalence Class (dpeaa)DE-He213 Complex Number (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Geometric Structure (dpeaa)DE-He213 Isomorphism Class (dpeaa)DE-He213 |
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Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
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Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
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10.1007/s00220-003-0930-5 |
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lie superalgebras based on $ 𝔤𝔩_{n} $ associated to the adjoint representation, and invariant geometric structures defined on them |
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Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
| abstract |
Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. © Springer-Verlag Berlin Heidelberg 2003 |
| abstractGer |
Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. © Springer-Verlag Berlin Heidelberg 2003 |
| abstract_unstemmed |
Abstract Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is $ 𝔤𝔩_{n} $ and whose odd module is $ 𝔤𝔩_{n} $ itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit $ ℤ_{2} $-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that $ ℤ_{2} $-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of $ 𝔤𝔩_{2} $ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) $ 𝔤𝔩_{2} $. © Springer-Verlag Berlin Heidelberg 2003 |
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| title_short |
Lie Superalgebras Based on $ 𝔤𝔩_{n} $ Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them |
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https://dx.doi.org/10.1007/s00220-003-0930-5 |
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Sánchez-Valenzuela, O.A. |
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10.1007/s00220-003-0930-5 |
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2024-07-04T02:38:39.108Z |
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| score |
7.399349 |