Vol. 306, No. 2, 2020

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$2$-categories of symmetric bimodules and their $2$-representations

Volodymyr Mazorchuk, Vanessa Miemietz and Xiaoting Zhang

Vol. 306 (2020), No. 2, 645–678

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.

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finite abelian group, symmetric bimodule, 2-category, simple transitive 2-representation
Mathematical Subject Classification 2010
Primary: 18D05
Received: 5 May 2019
Revised: 13 February 2020
Accepted: 13 February 2020
Published: 13 July 2020
Volodymyr Mazorchuk
Department of Mathematics
Uppsala University
Vanessa Miemietz
School of Mathematics
University of East Anglia
United Kingdom
Xiaoting Zhang
Academy for Multidisciplinary Studies
Capital Normal University