Operator Algebra Seminar

Weekly Operator Algebra Seminar

Speaker: Hannes Thiel (University of Münster)

Title: "Rigidity results for group algebras"

Abstract : Given a discrete group G, we study completions of the complex group algebra C[G]. We ask whether such completions recover the group.

For each 1≤p<∞, the left regular representation of G on lp(G) induces a representation of C[G] on lp(G) by left comvolution operators. The completion in the corresponding operator norm is called the reduced group Lp-operator algebra, denoted by Fpλ(G). For p=2, this is just the reduced group C*-algebra C*λ(G).

Let G and H be two groups such that Fpλ(G)\cong FpλH. Can we deduce G\cong H? Surprisingly, the answer is 'yes' if p≠2. For p=1, this was first obtained by Wendel in the 60's.

For p=2, the situation changes dramatically. There exist easy examples of non-isomorphic groups with isomorphic reduced group C*-algebras. Nevertheless, there are cases in which the group is remembered by its reduced group C*-algebra. I will report on recent work on such groups.

This talk is about joint work with E. Gardella, and joint work with S. Knudby and S. White.