The Classification of All Crossed Products H₄#k[Cn]
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Classification of All Crossed Products H₄#k[Cn]
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| Creator |
Agore, A.L.
Bontea, C.G. Militaru, G. |
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| 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.
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| Date |
2019-02-10T19:10:07Z
2019-02-10T19:10:07Z 2014 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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