Basic Hopf algebras and symmetric bimodules

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Hristova, Katerina and Miemietz, Vanessa (2023) Basic Hopf algebras and symmetric bimodules. Journal of Pure and Applied Algebra, 227 (7). ISSN 0022-4049

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Abstract

Motivated by the so-called H-cell reduction theorems, we investigate certain classes of bicategories which have only one H-cell apart from possibly the identity. We show that H_0-simple quasi fiab bicategories with unique H-cell H_0 are fusion categories. We further study two classes of non-semisimple quasi-fiab bicategories with a single H-cell apart from the identity. The first is $\cH_A$, indexed by a finite-dimensional radically graded basic Hopf algebra A, and the second is $\cG_A$, consisting of symmetric projective A-A-bimodules. We show that $\cH_A$ can be viewed as a 1-full subbicategory of $\cG_A$ and classify simple transitive birepresentations for $\cG_A$. We point out that the number of equivalence classes of the latter is finite, while that for $\cH_A$ is generally not.

Item Type:	Article
Additional Information:	Funding Information: The research for this article was supported by EPSRC grant EP/S017216/1.
Uncontrolled Keywords:	bicategory,hopf algebra,symmetric bimodule,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/2207.12983
Depositing User:	LivePure Connector
Date Deposited:	16 Jan 2023 18:30
Last Modified:	15 May 2023 01:00
URI:	https://ueaeprints.uea.ac.uk/id/eprint/90614
DOI:	10.1016/j.jpaa.2023.107328

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