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,...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2014 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2014
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146697 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747972055334912 |
|---|---|
| author | Agore, A.L. Bontea, C.G. Militaru, G. |
| author_facet | Agore, A.L. Bontea, C.G. Militaru, G. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T20:53:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146697 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:53:46Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Agore, A.L. Bontea, C.G. Militaru, G. 2019-02-10T19:10:07Z 2019-02-10T19:10:07Z 2014 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 https://nasplib.isofts.kiev.ua/handle/123456789/146697 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Classification of All Crossed Products H₄#k[Cn] Article published earlier |
| spellingShingle | The Classification of All Crossed Products H₄#k[Cn] Agore, A.L. Bontea, C.G. Militaru, G. |
| title | 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_short | The Classification of All Crossed Products H₄#k[Cn] |
| title_sort | classification of all crossed products h₄#k[cn] |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146697 |
| work_keys_str_mv | AT agoreal theclassificationofallcrossedproductsh4kcn AT bonteacg theclassificationofallcrossedproductsh4kcn AT militarug theclassificationofallcrossedproductsh4kcn AT agoreal classificationofallcrossedproductsh4kcn AT bonteacg classificationofallcrossedproductsh4kcn AT militarug classificationofallcrossedproductsh4kcn |