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Characterisation And Applications Of κ-Split Bimodules
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.ORCID iD: 0000-0002-4633-6218
Univ East Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2019 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 124, no 2, p. 161-178Article in journal (Refereed) Published
Abstract [en]

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]/(x(2), y(2), xy).

Place, publisher, year, edition, pages
2019. Vol. 124, no 2, p. 161-178
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-392859DOI: 10.7146/math.scand.a-111146ISI: 000478716400001OAI: oai:DiVA.org:uu-392859DiVA, id: diva2:1350056
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationGöran Gustafsson Foundation for Research in Natural Sciences and MedicineAvailable from: 2019-09-10 Created: 2019-09-10 Last updated: 2019-09-10Bibliographically approved

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Mazorchuk, VolodymyrZhang, Xiaoting

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