Operator algebra seminar

Speaker: Marcus de Chiffre (TU Dresden)

Title: Stability of asymptotic representations and non-approximable groups

Abstract: In this talk we provide new examples of stable groups and the first examples of non-approximable groups in the context of the Frobenius norm (the unnormalized Hilbert-Schmidt norm). A group is called stable if every asymptotic representation (a sequence of asymptotically multiplicative maps into the unitary matrices) can be perturbed to a sequence of genuine representations and approximable if there exists a separating asymptotic representation. We give a cohomological sufficient condition for a finitely presented group to be stable and use this, together with cohomology vanishing results by Garland and Ballmann-Swiatkowski, to provide examples of such groups. These examples, which are lattices in p-adic Lie groups, are residually finite and thus approximable, but some of them have non-approximable central extensions, as can be shown by mimicing methods of Deligne. The talk is based on joint work with Lev Glebsky, Alex Lubotzky and Andreas Thom.