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
Date:2021
Main Author: Shapiro, Ilya
Format: Article
Language:English
Published: Інститут математики НАН України 2021
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
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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).
first_indexed 2026-03-14T23:43:22Z
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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