Characterisation and applications of k-split bimodules

Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang

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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).
Original languageEnglish
Pages (from-to)161-178
Number of pages18
JournalMathematica Scandinavica
Issue number2
Publication statusPublished - 17 Jun 2019

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