Jason Crann, Carleton University & Universit ́e Lille I
“Amenability and injectivity of locally compact quantum groups”
As is well known, the equivalence between amenability of a locally compact group G and injectivity of its von Neumann algebra L(G) does not hold in general beyond [IN]-groups. In this talk, we will show that the equivalence persists for all locally compact groups if L(G) is considered as a T(L2(G))-module with respect to a natural action. In fact, we will prove an appropriate version of this result for every locally compact quantum group G. Time permitting, we will discuss further homological properties of T(L2(G))-modules and their connections to amenability. This is joint work with Matthias Neufang.