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

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

2003-12-15

arxiv.org/abs/math/0312283v2

Mathematics

Operator Algebras

Substantial changes from the previous version

Scientific paper

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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