Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
The Classification of All Crossed Products H₄#k[Cn]
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
The Classification of All Crossed Products H₄#k[Cn]
Інший ID:
2010 Mathematics Subject Classification: 16T10; 16T05; 16S40
DOI:10.3842/SIGMA.2014.049
DOI:10.3842/SIGMA.2014.049
Посилання:
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.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
The authors would like to thank the referees for their comments and suggestions that substantially
improved the first version of this paper. A.L. Agore is research fellow ‘Aspirant’ of
FWO-Vlaanderen. This work was supported by a grant of the Romanian National Authority
for Scientific Research, CNCS-UEFISCDI, grant no. 88/05.10.2011.
Дата:
2014
Переглядів:
501
Завантажень:
244
Анотація:
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.
