Extension problems for representations of crossed-product C*-algebras

2005/02/08 by Astrid an Huef, Huef, Astrid an, S. Kaliszewski +5 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Spectral Theory in Mathematical Physics #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0502151

Added a proposition and a lemma

arxiv created 2006/11/09 · arxiv updated 2009/12/01

Abstract

We consider the following problem. Suppose α is an action of a locally compact group G on a C^*-algebra A, H is a closed subgroup of G, and (π,U) is a covariant representation of (A,H,α). For which closed subgroups K containing H is there a covariant representation (π,V) of (A,K,α) such that V|_H=U? We answer this problem by providing a criterion involving the induced representation of (A,G,α). We then consider the dual problem for coactions of locally compact groups.

Cited by

• Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces

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