Completions of group algebras, growth and nuclearity

03/10/2016 - 15:30
03/10/2016 - 16:30
Simone Gutt, (Université Libre de Bruxelles)
McGill University, Burnside 719A, 805 Sherbrooke West - McGill University

If G is a finitely generated infinite group, we define completions Asigma(G) of the group algebra C[G] in the space of formal power series in G, using norms which are defined using a growth functionsigma, i.e. an unbounded nowhere decreasing function sigma: N o [1,infty) which is submultiplicative (i.e. sigma(n + m) <= sigma(n)sigma(m)) or almost submultiplicative (i.e. for every epsilon > 0, there exists a constant c > 0 such that sigma(n + m) <= csigma(n)^{1+epsilon} sigma(m)^{1+epsilon}. We show that Asigma(G) is a Frechet-Hopf *-algebra. We relate nuclearity of such a completion to a growth property of the group. This is joint work with Michel Cahen and Stefan Waldmann.

Last edited by on Thu, 03/03/2016 - 15:26