Operator algebra Seminar by Paul Jolissaint

Relative inner amenability and relative property gamma

We say that a subgroup H of a group G is inner amenable relative to G if it is proper and if its action by conjugation on GH admits an invariant mean. We will discuss this property and present families of examples. The analoguous relative property gamma for subfactors in type II_1 factors will also be discussed. In particular, it will be compared to D. Bisch's property gamma for an inclusion of type II_1 factors, and a characterization of non-Kazhdan's groups will be given.