Ideal structure of C-algebras of commuting local homeomorphisms

We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale groupoids associated to finite families of commuting local homeomo...

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Published in:arXiv.org 2023-12
Main Authors: Brix, Kevin Aguyar, Toke Meier Carlsen, Sims, Aidan
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Algebra
Group theory
Topology
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Sims, Aidan
description We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale groupoids associated to finite families of commuting local homeomorphisms. Our results unify and recover all known results on ideal structure for crossed products of commutative C*-algebras by free abelian groups, for graph C*-algebras, and for Katsura's topological graph C*-algebras.
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subjects Algebra
Group theory
Topology
title Ideal structure of C-algebras of commuting local homeomorphisms
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