*-homomorphisms between groupoid C*-algebras

Fuyuta Komura

-homomorphisms between groupoid C-algebras

Operator Algebras 2023-08-24 v3

Authors: Fuyuta Komura

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.

Keywords

c*-algebra c*-algebras crossed products

Cite

@article{arxiv.2302.10405,
  title  = {*-homomorphisms between groupoid C*-algebras},
  author = {Fuyuta Komura},
  journal= {arXiv preprint arXiv:2302.10405},
  year   = {2023}
}

Comments

24 pages, with minor changes(ver2). In ver3, assumptions about effectiveness of \'etale groupoids are relaxed. arXiv admin note: text overlap with arXiv:2206.11713