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Cocompact Amenable Closed Subgroups: Weakly Inequivalent Representations in the Left-regular Representation by Raum, Sven is a scholarly article available to read on EtoBox.

What is Cocompact Amenable Closed Subgroups: Weakly Inequivalent Representations in the Left-regular Representation about?

We show that if $H \leq G$ 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.

Author

Raum, Sven

Published

2015

Language

EN