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 |
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| 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| Summary: | 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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| ISSN: | 1815-0659 |