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
    Depositing User: Pure Connector
    Date Deposited: 26 Feb 2018 12:34
    Last Modified: 03 Jul 2019 09:30
    URI: https://ueaeprints.uea.ac.uk/id/eprint/66365
    DOI: 10.7146/math.scand.a-111146

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