Characterisation and applications of k-split bimodules

Mazorchuk, Volodymyr, Miemietz, Vanessa and Zhang, Xiaoting (2019) Characterisation and applications of k-split bimodules. Mathematica Scandinavica, 124 (2). pp. 161-178. ISSN 1903-1807

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Abstract

We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projective module. The main result is that all such bimodules are k-split in the sense that they factor (inside the tensor category of bimodules) over k-vector spaces. As one application, we show that any simple 2-category has a faithful 2-representation inside the 2-category of k-split bimodules. As another application, we classify simple transitive 2-representations of the 2-category of projective bimodules over the algebra k[x, y]/(x2, y2, xy).

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	26 Feb 2018 12:34
Last Modified:	07 Nov 2024 12:40
URI:	https://ueaeprints.uea.ac.uk/id/eprint/66365
DOI:	10.7146/math.scand.a-111146

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