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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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