Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras
We apply categorical machinery to the problem of defining anti-Yetter-Drinfeld modules for quasi-Hopf algebras. While a definition of Yetter-Drinfeld modules in this setting, extracted from their categorical interpretation as the center of the monoidal category of modules, has been given, none was a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209859 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras / I. Kobyzev, I. Shapiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706240469073920 |
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| author | Kobyzev, I. Shapiro, I. |
| author_facet | Kobyzev, I. Shapiro, I. |
| citation_txt | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras / I. Kobyzev, I. Shapiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We apply categorical machinery to the problem of defining anti-Yetter-Drinfeld modules for quasi-Hopf algebras. While a definition of Yetter-Drinfeld modules in this setting, extracted from their categorical interpretation as the center of the monoidal category of modules, has been given, none was available for the anti-Yetter-Drinfeld modules that serve as coefficients for a Hopf cyclic type cohomology theory for quasi-Hopf algebras. This is a follow-up paper to the authors' previous effort that addressed the somewhat different case of anti-Yetter-Drinfeld contramodule coefficients in this and in the Hopf algebroid setting.
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| first_indexed | 2025-12-07T16:58:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209859 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:58:14Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kobyzev, I. Shapiro, I. 2025-11-27T14:58:08Z 2018 Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras / I. Kobyzev, I. Shapiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 18D10; 18E05; 19D55; 16T05 arXiv: 1804.02031 https://nasplib.isofts.kiev.ua/handle/123456789/209859 https://doi.org/10.3842/SIGMA.2018.098 We apply categorical machinery to the problem of defining anti-Yetter-Drinfeld modules for quasi-Hopf algebras. While a definition of Yetter-Drinfeld modules in this setting, extracted from their categorical interpretation as the center of the monoidal category of modules, has been given, none was available for the anti-Yetter-Drinfeld modules that serve as coefficients for a Hopf cyclic type cohomology theory for quasi-Hopf algebras. This is a follow-up paper to the authors' previous effort that addressed the somewhat different case of anti-Yetter-Drinfeld contramodule coefficients in this and in the Hopf algebroid setting. The authors wish to thank Masoud Khalkhali for stimulating questions and discussions. The research of the second author was supported in part by the NSERC Discovery Grant number 406709. In addition, we thank the referees for their helpful corrections. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras Article published earlier |
| spellingShingle | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras Kobyzev, I. Shapiro, I. |
| title | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras |
| title_full | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras |
| title_fullStr | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras |
| title_full_unstemmed | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras |
| title_short | Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras |
| title_sort | anti-yetter-drinfeld modules for quasi-hopf algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209859 |
| work_keys_str_mv | AT kobyzevi antiyetterdrinfeldmodulesforquasihopfalgebras AT shapiroi antiyetterdrinfeldmodulesforquasihopfalgebras |