Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences

2025/06/24 by Meyer, Ralf · 2 citations
#46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2506.19569

Abstract

A groupoid correspondence on an etale, locally compact groupoid induces a C*-correspondence on its groupoid C*-algebra. We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid. We describe this groupoid explicitly and characterise it by a universal property that specifies its actions on topological spaces. Our construction unifies the construction of groupoids underlying the C*-algebras of topological graphs and self-similar groups.

Citations

• Graph morphisms as groupoid actors
• Homology and K-theory for self-similar actions of groups and groupoids
• Groupoid models for diagrams of groupoid correspondences
• Self-similar graphs, a unified treatment of Katsura and Nekrashevych\n C*-algebras
• Inverse Semigroups and Combinatorial C*-Algebras
• Non-Hausdorff groupoids, proper actions and K-theory
• Graph inverse semigroups, groupoids and their C*-algebras

Cited by

• Graph morphisms as groupoid actors
• Bicategories of C*-correspondences as Dwyer-Kan localisations

Related

• Groupoid actions on C^*-correspondences
• Self-Similar k-Graph C*-Algebras
• C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
• Groupoid models for diagrams of groupoid correspondences
• Topological construction of C^*-correspondences for groupoid C^*-algebras