Operator Algebra Seminar

Abstract: A group G is called W*-superrigid if it is completely remembered by its group von Neumann algebra in the following sense: any other group with the same group von Neumann algebra must be isomorphic to G. By now, there are many examples of W*-superrigid groups. Of course, a group von Neumann algebra is also a compact quantum group, hence one can ask whether superrigidity also holds in this larger class. Surprisingly, many of the typical W*-superrid groups in the literature fail to remain superrigid as quantum groups. I will present a recent joint work with Stefaan Vaes where we prove certain (cohomological) obstructions to `quantum W*-superrigidity’. We also build on previous work to find the first examples of discrete groups and (non-cocommutative) compact quantum groups which are quantum W*-superrigid.