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

Abstract

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

Added a proposition and a lemma

Cited by in corpus (1)

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