2-categories of symmetric bimodules and their 2-representations

Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang

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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 languageEnglish
Pages (from-to)645-678
Number of pages34
JournalPacific Journal of Mathematics
Volume306
Issue number2
DOIs
Publication statusPublished - 13 Jul 2020

Keywords

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

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