Basic Hopf algebras and symmetric bimodules

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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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
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Depositing User: LivePure Connector
Date Deposited: 16 Jan 2023 18:30
Last Modified: 15 May 2023 01:00
DOI: 10.1016/j.jpaa.2023.107328


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