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

Astrid an Huef·S. Kaliszewski·Iain Raeburn·Dana P. Williams
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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.

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Astrid an Huef, S. Kaliszewski, Iain Raeburn, Dana P. Williams. 2006-11-09. Extension problems for representations of crossed-product C*-algebras. https://arxiv.org/abs/math/0502151

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