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

Huef, Astrid an; Kaliszewski, S.; Raeburn, Iain; Williams, Dana P.

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

Authors

Description

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.
Added a proposition and a lemma