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$2$-categories of
symmetric bimodules and their $2$-representations
Volodymyr Mazorchuk, Vanessa Miemietz and Xiaoting Zhang |
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Vol. 306 (2020), No. 2, 645–678
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Abstract |
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In this article we analyze the structure of -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 -category is fiat (in the sense of Mazorchuk and Miemietz (2011)) and classify simple transitive -representations of this -category (under some mild technical assumption). We also study several classes of examples in detail. |
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Keywords
finite abelian group, symmetric bimodule, 2-category,
simple transitive 2-representation
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Mathematical Subject Classification 2010
Primary: 18D05
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Milestones
Received: 5 May 2019
Revised: 13 February 2020
Accepted: 13 February 2020
Published: 13 July 2020
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Authors |
| Volodymyr Mazorchuk | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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| Vanessa Miemietz | |
| School of Mathematics University of East Anglia Norwich United Kingdom |
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| Xiaoting Zhang | |
| Academy for Multidisciplinary
Studies Capital Normal University Beijing China |
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