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Extension problems and non-abelian duality for $C^*$-algebras

Astrid an Huef·S. Kaliszewski·Iain Raeburn
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Abstract

Suppose that $H$ is a closed subgroup of a locally compact group $G$. We show that a unitary representation $U$ of $H$ is the restriction of a unitary representation of $G$ if and only if a dual representation $\hat U$ of a crossed product $C^*(G)\rtimes (G/H)$ is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-abelian duality for crossed products of $C^*$-algebras.

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Astrid an Huef, S. Kaliszewski, Iain Raeburn. 2006-11-09. Extension problems and non-abelian duality for $C^*$-algebras. https://arxiv.org/abs/math/0312283

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