Mixed vs Stable Anti-Yetter-Drinfeld Contramodules
We examine the cyclic homology of the monoidal category of modules over a finite-dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules....
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211323 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules. Ilya Shapiro. SIGMA 17 (2021), 026, 10 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862636079445704704 |
|---|---|
| author | Shapiro, Ilya |
| author_facet | Shapiro, Ilya |
| citation_txt | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules. Ilya Shapiro. SIGMA 17 (2021), 026, 10 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We examine the cyclic homology of the monoidal category of modules over a finite-dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules. Namely, we show that Sweedler's Hopf algebra provides an example where mixed complexes in the category of stable anti-Yetter-Drinfeld contramodules (previously studied) are not equivalent, as differential graded categories to the category of mixed anti-Yetter-Drinfeld contramodules (recently introduced).
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| first_indexed | 2026-03-14T23:43:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211323 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T23:43:22Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Shapiro, Ilya 2025-12-29T11:11:58Z 2021 Mixed vs Stable Anti-Yetter-Drinfeld Contramodules. Ilya Shapiro. SIGMA 17 (2021), 026, 10 pages 1815-0659 2020 Mathematics Subject Classification: 16E35; 16T05; 18G90; 19D55 arXiv:2010.02768 https://nasplib.isofts.kiev.ua/handle/123456789/211323 https://doi.org/10.3842/SIGMA.2021.026 We examine the cyclic homology of the monoidal category of modules over a finite-dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules. Namely, we show that Sweedler's Hopf algebra provides an example where mixed complexes in the category of stable anti-Yetter-Drinfeld contramodules (previously studied) are not equivalent, as differential graded categories to the category of mixed anti-Yetter-Drinfeld contramodules (recently introduced). This research was supported in part by the NSERC Discovery Grant number 406709. The author wishes to thank the referees for their many helpful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Mixed vs Stable Anti-Yetter-Drinfeld Contramodules Article published earlier |
| spellingShingle | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules Shapiro, Ilya |
| title | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules |
| title_full | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules |
| title_fullStr | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules |
| title_full_unstemmed | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules |
| title_short | Mixed vs Stable Anti-Yetter-Drinfeld Contramodules |
| title_sort | mixed vs stable anti-yetter-drinfeld contramodules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211323 |
| work_keys_str_mv | AT shapiroilya mixedvsstableantiyetterdrinfeldcontramodules |