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arXiv · 2302.10405

*-homomorphisms between groupoid C*-algebras

Fuyuta Komura
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Abstract

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some assumptions. Then we prove C*-rigidity results for \'etale groupoids which are not necessarily effective. As another application, we investigate certain subgroups of the automorphism groups of groupoid C*-algebras. More precisely, we show that the groups of automorphisms that globally preserve the function algebras on the unit spaces are isomorphic to certain semidirect product groups. As a corollary, we show that, if group actions on groupoid C*-algebras fix the function algebras on the unit spaces, then the actions factors through the abelianizations of the acting groups.

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Fuyuta Komura. 2023-02-21. *-homomorphisms between groupoid C*-algebras. https://arxiv.org/abs/2302.10405

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