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September 2020 Bimodules over uniformly oriented A n quivers with radical square zero
Volodymyr Mazorchuk, Xiaoting Zhang
Kyoto J. Math. 60(3): 965-995 (September 2020). DOI: 10.1215/21562261-2019-0052

Abstract

The only connected finite-dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented A n -quivers modulo the radical square zero relations. For such algebras we study the (finitary) tensor category of bimodules. We describe the cell structure of this tensor category, we determine existing adjunctions between its 1 -morphisms, and we find a minimal generating set with respect to the tensor structure. We also prove that, for the algebras mentioned above, every simple transitive 2 -representation of the 2 -category of projective bimodules is equivalent to a cell 2 -representation.

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Volodymyr Mazorchuk. Xiaoting Zhang. "Bimodules over uniformly oriented A n quivers with radical square zero." Kyoto J. Math. 60 (3) 965 - 995, September 2020. https://doi.org/10.1215/21562261-2019-0052

Information

Received: 6 April 2017; Revised: 27 October 2017; Accepted: 15 February 2018; Published: September 2020
First available in Project Euclid: 12 August 2020

MathSciNet: MR4134355
Digital Object Identifier: 10.1215/21562261-2019-0052

Subjects:
Primary: 18D05
Secondary: 16D20, 16G10

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 3 • September 2020
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