The Classification of All Crossed Products H₄#k[Cn]
Using the computational approach introduced in [Agore A.L., Bontea C.G., Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages] we classify all coalgebra split extensions of H₄ by k[Cn], where Cn is the cyclic group of order n and H₄ is Sweedler's 4-dimensional Hopf algebra. Equivalently,...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2014 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146697 |
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| Цитувати: | The Classification of All Crossed Products H₄#k[Cn] / A.L. Agore, C.G. Bontea, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146697 |
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irk-123456789-1466972019-02-11T01:23:22Z The Classification of All Crossed Products H₄#k[Cn] Agore, A.L. Bontea, C.G. Militaru, G. Using the computational approach introduced in [Agore A.L., Bontea C.G., Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages] we classify all coalgebra split extensions of H₄ by k[Cn], where Cn is the cyclic group of order n and H₄ is Sweedler's 4-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras H₄#k[Cn] by explicitly computing two classifying objects: the cohomological 'group' H²(k[Cn],H₄) and CRP(k[Cn],H₄):= the set of types of isomorphisms of all crossed products H₄#k[Cn]. More precisely, all crossed products H₄#k[Cn] are described by generators and relations and classified: they are 4n-dimensional quantum groups H₄n,λ,t, parameterized by the set of all pairs (λ,t) consisting of an arbitrary unitary map t:Cn→C₂ and an n-th root λ of ±1. As an application, the group of Hopf algebra automorphisms of H₄n,λ,t is explicitly described. 2014 Article The Classification of All Crossed Products H₄#k[Cn] / A.L. Agore, C.G. Bontea, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T10; 16T05; 16S40 DOI:10.3842/SIGMA.2014.049 http://dspace.nbuv.gov.ua/handle/123456789/146697 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Using the computational approach introduced in [Agore A.L., Bontea C.G., Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages] we classify all coalgebra split extensions of H₄ by k[Cn], where Cn is the cyclic group of order n and H₄ is Sweedler's 4-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras H₄#k[Cn] by explicitly computing two classifying objects: the cohomological 'group' H²(k[Cn],H₄) and CRP(k[Cn],H₄):= the set of types of isomorphisms of all crossed products H₄#k[Cn]. More precisely, all crossed products H₄#k[Cn] are described by generators and relations and classified: they are 4n-dimensional quantum groups H₄n,λ,t, parameterized by the set of all pairs (λ,t) consisting of an arbitrary unitary map t:Cn→C₂ and an n-th root λ of ±1. As an application, the group of Hopf algebra automorphisms of H₄n,λ,t is explicitly described. |
| format |
Article |
| author |
Agore, A.L. Bontea, C.G. Militaru, G. |
| spellingShingle |
Agore, A.L. Bontea, C.G. Militaru, G. The Classification of All Crossed Products H₄#k[Cn] Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Agore, A.L. Bontea, C.G. Militaru, G. |
| author_sort |
Agore, A.L. |
| title |
The Classification of All Crossed Products H₄#k[Cn] |
| title_short |
The Classification of All Crossed Products H₄#k[Cn] |
| title_full |
The Classification of All Crossed Products H₄#k[Cn] |
| title_fullStr |
The Classification of All Crossed Products H₄#k[Cn] |
| title_full_unstemmed |
The Classification of All Crossed Products H₄#k[Cn] |
| title_sort |
classification of all crossed products h₄#k[cn] |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146697 |
| citation_txt |
The Classification of All Crossed Products H₄#k[Cn] / A.L. Agore, C.G. Bontea, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:26Z |
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