The Automorphism Group of a Simple Tracially AI Algebra
Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algeb...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ng, Ping Wong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 280(2008), 2 vom: 08. Apr., Seite 427-444 |
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| Übergeordnetes Werk: |
volume:280 ; year:2008 ; number:2 ; day:08 ; month:04 ; pages:427-444 |
| Links: |
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| DOI / URN: |
10.1007/s00220-008-0478-5 |
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| Katalog-ID: |
SPR002341956 |
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| 100 | 1 | |a Ng, Ping Wong |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Automorphism Group of a Simple Tracially AI Algebra |
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| 520 | |a Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. | ||
| 650 | 4 | |a Exact Sequence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Automorphism Group |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Inverse Limit |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stable Rank |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Torsion Group |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Ruiz, Efren |4 aut | |
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10.1007/s00220-008-0478-5 doi (DE-627)SPR002341956 (SPR)s00220-008-0478-5-e DE-627 ger DE-627 rakwb eng Ng, Ping Wong verfasserin aut The Automorphism Group of a Simple Tracially AI Algebra 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 Ruiz, Efren aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 280(2008), 2 vom: 08. Apr., Seite 427-444 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:280 year:2008 number:2 day:08 month:04 pages:427-444 https://dx.doi.org/10.1007/s00220-008-0478-5 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 280 2008 2 08 04 427-444 |
| spelling |
10.1007/s00220-008-0478-5 doi (DE-627)SPR002341956 (SPR)s00220-008-0478-5-e DE-627 ger DE-627 rakwb eng Ng, Ping Wong verfasserin aut The Automorphism Group of a Simple Tracially AI Algebra 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 Ruiz, Efren aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 280(2008), 2 vom: 08. Apr., Seite 427-444 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:280 year:2008 number:2 day:08 month:04 pages:427-444 https://dx.doi.org/10.1007/s00220-008-0478-5 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 280 2008 2 08 04 427-444 |
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10.1007/s00220-008-0478-5 doi (DE-627)SPR002341956 (SPR)s00220-008-0478-5-e DE-627 ger DE-627 rakwb eng Ng, Ping Wong verfasserin aut The Automorphism Group of a Simple Tracially AI Algebra 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 Ruiz, Efren aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 280(2008), 2 vom: 08. Apr., Seite 427-444 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:280 year:2008 number:2 day:08 month:04 pages:427-444 https://dx.doi.org/10.1007/s00220-008-0478-5 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 280 2008 2 08 04 427-444 |
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10.1007/s00220-008-0478-5 doi (DE-627)SPR002341956 (SPR)s00220-008-0478-5-e DE-627 ger DE-627 rakwb eng Ng, Ping Wong verfasserin aut The Automorphism Group of a Simple Tracially AI Algebra 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 Ruiz, Efren aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 280(2008), 2 vom: 08. Apr., Seite 427-444 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:280 year:2008 number:2 day:08 month:04 pages:427-444 https://dx.doi.org/10.1007/s00220-008-0478-5 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 280 2008 2 08 04 427-444 |
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10.1007/s00220-008-0478-5 doi (DE-627)SPR002341956 (SPR)s00220-008-0478-5-e DE-627 ger DE-627 rakwb eng Ng, Ping Wong verfasserin aut The Automorphism Group of a Simple Tracially AI Algebra 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 Ruiz, Efren aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 280(2008), 2 vom: 08. Apr., Seite 427-444 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:280 year:2008 number:2 day:08 month:04 pages:427-444 https://dx.doi.org/10.1007/s00220-008-0478-5 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 280 2008 2 08 04 427-444 |
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Enthalten in Communications in mathematical physics 280(2008), 2 vom: 08. Apr., Seite 427-444 volume:280 year:2008 number:2 day:08 month:04 pages:427-444 |
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Ng, Ping Wong |
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The Automorphism Group of a Simple Tracially AI Algebra Exact Sequence (dpeaa)DE-He213 Automorphism Group (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Stable Rank (dpeaa)DE-He213 Torsion Group (dpeaa)DE-He213 |
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automorphism group of a simple tracially ai algebra |
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The Automorphism Group of a Simple Tracially AI Algebra |
| abstract |
Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. © Springer-Verlag 2008 |
| abstractGer |
Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. © Springer-Verlag 2008 |
| abstract_unstemmed |
Abstract The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that %${\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}%$ is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, %${\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}%$ is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group %${\rm{Aut}(\underline{K}(A))_{+,1}}%$. © Springer-Verlag 2008 |
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The Automorphism Group of a Simple Tracially AI Algebra |
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https://dx.doi.org/10.1007/s00220-008-0478-5 |
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Ruiz, Efren |
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10.1007/s00220-008-0478-5 |
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2024-07-04T02:40:40.415Z |
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