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

[img]
Preview
PDF (Accepted manuscript) - Submitted Version
Download (203kB) | Preview

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
Depositing User: Pure Connector
Date Deposited: 26 Feb 2018 12:34
Last Modified: 18 Nov 2019 20:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/66365
DOI: 10.7146/math.scand.a-111146

Actions (login required)

View Item View Item