Characterisation and applications of k-split bimodules

• Volodymyr Mazorchuk ^[1] ; Vanessa Miemietz ^[2] ; Xiaoting Zhang ^[1]
  1. [1] Uppsala University

     Uppsala University

     Uppsala domkyrkoförs., Suecia

     
  2. [2] University of East Anglia

     University of East Anglia

     Norwich District, Reino Unido

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 2, 2019, págs. 161-178
• Idioma: inglés
• DOI: 10.7146/math.scand.a-111146
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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).