TY - JOUR
AU - Volodymyr Mazorchuk
AU - Vanessa Miemietz
AU - Xiaoting Zhang
PY - 2019/06/17
Y2 - 2020/06/01
TI - Characterisation and applications of $\Bbbk$-split bimodules
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 124
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-111146
UR - https://www.mscand.dk/article/view/111146
AB - 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 $\Bbbk $-split in the sense that they factor (inside the tensor category of bimodules) over $\Bbbk $-vector spaces. As one application, we show that any simple $2$-category has a faithful $2$-representation inside the $2$-category of $\Bbbk $-split bimodules. As another application, we classify simple transitive $2$-representations of the $2$-category of projective bimodules over the algebra $\Bbbk [x,y]/(x^2,y^2,xy)$.
ER -