Cocompact amenable closed subgroups: weakly inequivalent representations in the left-regular representation

2015/10/21 by Raum, Sven
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Primary 22D10 #Secondary 22D25

paper · doi:10.48550/arxiv.1510.06215

Abstract

We show that if H ≤ G is a closed amenable and cocompact subgroup of a unimodular locally compact group, then the reduced group C*-algebra of G is not simple. Equivalently, there are unitary representations of G that are weakly contained in the left-regular representation, but not weakly equivalent to it. We discuss applications of this result and pose the problem to construct non-discrete topologically simple groups with a cocompact amenable closed subgroup but without a Gelfand pair.

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