Characterisation and applications of -split bimodules - Mazorchuk, Volodymyr; Miemietz, Vanessa; Zhang, Xiaoting (MATHEMATICA SCANDINAVICA, 2019)
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 -split in the sense that they factor (inside the tensor category of bimodules) over -vector spaces. As one application, we show that any simple 2-category has a faithful 2-representation inside the 2-category of -split bimodules. As another application, we classify simple transitive 2-representations of the 2-category of projective bimodules over the algebra [x,y]/(x^2,y^2,xy).