TY - JOUR

T1 - Characterisation and applications of k-split bimodules

AU - Mazorchuk, Volodymyr

AU - Miemietz, Vanessa

AU - Zhang, Xiaoting

PY - 2019/6/17

Y1 - 2019/6/17

N2 - 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).

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 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).

UR - http://www.scopus.com/inward/record.url?scp=85069713906&partnerID=8YFLogxK

U2 - 10.7146/math.scand.a-111146

DO - 10.7146/math.scand.a-111146

M3 - Article

VL - 124

SP - 161

EP - 178

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 2

ER -