Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve
Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhang, Xinru [verfasserIn] Sun, Hua [verfasserIn] Chen, Huixiang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© Peking University 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Frontiers of mathematics - Springer Berlin Heidelberg, 2023, 19(2024), 4 vom: 05. Apr., Seite 691-710 |
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| Übergeordnetes Werk: |
volume:19 ; year:2024 ; number:4 ; day:05 ; month:04 ; pages:691-710 |
| Links: |
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| DOI / URN: |
10.1007/s11464-022-0293-x |
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| Katalog-ID: |
SPR056434723 |
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| 520 | |a Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. | ||
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| 650 | 4 | |a Green algebra |7 (dpeaa)DE-He213 | |
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| 700 | 1 | |a Chen, Huixiang |e verfasserin |4 aut | |
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10.1007/s11464-022-0293-x doi (DE-627)SPR056434723 (SPR)s11464-022-0293-x-e DE-627 ger DE-627 rakwb eng 510 VZ Zhang, Xinru verfasserin aut Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Peking University 2024 Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. Hopf algebra (dpeaa)DE-He213 Radford Hopf algebra (dpeaa)DE-He213 Green ring (dpeaa)DE-He213 Green algebra (dpeaa)DE-He213 automorphism group (dpeaa)DE-He213 Sun, Hua verfasserin aut Chen, Huixiang verfasserin aut Enthalten in Frontiers of mathematics Springer Berlin Heidelberg, 2023 19(2024), 4 vom: 05. Apr., Seite 691-710 Online-Ressource (DE-627)1839392819 (DE-600)3154304-2 2731-8656 nnns volume:19 year:2024 number:4 day:05 month:04 pages:691-710 https://dx.doi.org/10.1007/s11464-022-0293-x X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_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_2118 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2024 4 05 04 691-710 |
| spelling |
10.1007/s11464-022-0293-x doi (DE-627)SPR056434723 (SPR)s11464-022-0293-x-e DE-627 ger DE-627 rakwb eng 510 VZ Zhang, Xinru verfasserin aut Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Peking University 2024 Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. Hopf algebra (dpeaa)DE-He213 Radford Hopf algebra (dpeaa)DE-He213 Green ring (dpeaa)DE-He213 Green algebra (dpeaa)DE-He213 automorphism group (dpeaa)DE-He213 Sun, Hua verfasserin aut Chen, Huixiang verfasserin aut Enthalten in Frontiers of mathematics Springer Berlin Heidelberg, 2023 19(2024), 4 vom: 05. Apr., Seite 691-710 Online-Ressource (DE-627)1839392819 (DE-600)3154304-2 2731-8656 nnns volume:19 year:2024 number:4 day:05 month:04 pages:691-710 https://dx.doi.org/10.1007/s11464-022-0293-x X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_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_2118 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2024 4 05 04 691-710 |
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10.1007/s11464-022-0293-x doi (DE-627)SPR056434723 (SPR)s11464-022-0293-x-e DE-627 ger DE-627 rakwb eng 510 VZ Zhang, Xinru verfasserin aut Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Peking University 2024 Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. Hopf algebra (dpeaa)DE-He213 Radford Hopf algebra (dpeaa)DE-He213 Green ring (dpeaa)DE-He213 Green algebra (dpeaa)DE-He213 automorphism group (dpeaa)DE-He213 Sun, Hua verfasserin aut Chen, Huixiang verfasserin aut Enthalten in Frontiers of mathematics Springer Berlin Heidelberg, 2023 19(2024), 4 vom: 05. Apr., Seite 691-710 Online-Ressource (DE-627)1839392819 (DE-600)3154304-2 2731-8656 nnns volume:19 year:2024 number:4 day:05 month:04 pages:691-710 https://dx.doi.org/10.1007/s11464-022-0293-x X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_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_2118 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2024 4 05 04 691-710 |
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10.1007/s11464-022-0293-x doi (DE-627)SPR056434723 (SPR)s11464-022-0293-x-e DE-627 ger DE-627 rakwb eng 510 VZ Zhang, Xinru verfasserin aut Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Peking University 2024 Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. Hopf algebra (dpeaa)DE-He213 Radford Hopf algebra (dpeaa)DE-He213 Green ring (dpeaa)DE-He213 Green algebra (dpeaa)DE-He213 automorphism group (dpeaa)DE-He213 Sun, Hua verfasserin aut Chen, Huixiang verfasserin aut Enthalten in Frontiers of mathematics Springer Berlin Heidelberg, 2023 19(2024), 4 vom: 05. Apr., Seite 691-710 Online-Ressource (DE-627)1839392819 (DE-600)3154304-2 2731-8656 nnns volume:19 year:2024 number:4 day:05 month:04 pages:691-710 https://dx.doi.org/10.1007/s11464-022-0293-x X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_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_2118 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2024 4 05 04 691-710 |
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10.1007/s11464-022-0293-x doi (DE-627)SPR056434723 (SPR)s11464-022-0293-x-e DE-627 ger DE-627 rakwb eng 510 VZ Zhang, Xinru verfasserin aut Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Peking University 2024 Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. Hopf algebra (dpeaa)DE-He213 Radford Hopf algebra (dpeaa)DE-He213 Green ring (dpeaa)DE-He213 Green algebra (dpeaa)DE-He213 automorphism group (dpeaa)DE-He213 Sun, Hua verfasserin aut Chen, Huixiang verfasserin aut Enthalten in Frontiers of mathematics Springer Berlin Heidelberg, 2023 19(2024), 4 vom: 05. Apr., Seite 691-710 Online-Ressource (DE-627)1839392819 (DE-600)3154304-2 2731-8656 nnns volume:19 year:2024 number:4 day:05 month:04 pages:691-710 https://dx.doi.org/10.1007/s11464-022-0293-x X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_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_2118 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2024 4 05 04 691-710 |
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English |
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Enthalten in Frontiers of mathematics 19(2024), 4 vom: 05. Apr., Seite 691-710 volume:19 year:2024 number:4 day:05 month:04 pages:691-710 |
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Enthalten in Frontiers of mathematics 19(2024), 4 vom: 05. Apr., Seite 691-710 volume:19 year:2024 number:4 day:05 month:04 pages:691-710 |
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Hopf algebra Radford Hopf algebra Green ring Green algebra automorphism group |
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Zhang, Xinru @@aut@@ Sun, Hua @@aut@@ Chen, Huixiang @@aut@@ |
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Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve |
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Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. © Peking University 2024 |
| abstractGer |
Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. © Peking University 2024 |
| abstract_unstemmed |
Abstract Let H be the Radford Hopf algebra of dimension twelve over a field $$\mathbb{k}$$. In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. © Peking University 2024 |
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In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product $ ℂ^{x} $ × S4, where $ ℂ^{x} $ is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hopf algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Radford Hopf algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Green ring</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Green algebra</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="700" ind1="1" ind2=" "><subfield code="a">Sun, Hua</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chen, Huixiang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Frontiers of mathematics</subfield><subfield code="d">Springer Berlin Heidelberg, 2023</subfield><subfield code="g">19(2024), 4 vom: 05. Apr., Seite 691-710</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)1839392819</subfield><subfield code="w">(DE-600)3154304-2</subfield><subfield code="x">2731-8656</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:19</subfield><subfield code="g">year:2024</subfield><subfield code="g">number:4</subfield><subfield code="g">day:05</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:691-710</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s11464-022-0293-x</subfield><subfield code="m">X:SPRINGER</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_0</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield 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