2-categories of symmetric bimodules and their 2-representations

Volodymyr Mazorchuk; Vanessa Miemietz; Xiaoting Zhang

doi:10.2140/pjm.2020.306.645

2-categories of symmetric bimodules and their 2-representations

Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang

Algebra and Combinatorics

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Abstract

In this article we analyze the structure of 2-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting 2-category is fiat (in the sense of Mazorchuk and Miemietz (2011)) and classify simple transitive 2-representations of this 2-category (under some mild technical assumption). We also study several classes of examples in detail.

Original language	English
Pages (from-to)	645-678
Number of pages	34
Journal	Pacific Journal of Mathematics
Volume	306
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2020.306.645
Publication status	Published - 13 Jul 2020

Keywords

2-category
finite abelian group
simple transitive 2-representation
symmetric bimodule

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10.2140/pjm.2020.306.645

Accepted_ManuscriptAccepted author manuscript, 499 KB

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2-categories of symmetric bimodules and their 2-representations

Abstract

Keywords

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Vanessa Miemietz

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