Ulrik Enstad: Z-stability of twisted group C*-algebras

Abstract: I will present recent joint work with Eduard Vilalta. Z-stability is an important property in the classification program for nuclear C*-algebras. We prove that the twisted group C*-algebra of a finitely generated nilpotent group is Z-stable if and only if it is nowhere scattered, a condition that we characterize in terms of the given group and 2-cocycle. As a main application, we prove new converses to the Balian-Low Theorem for projective, square-integrable representations of nilpotent Lie groups.