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arXiv · 2506.19569

Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences

Ralf Meyer
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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.

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Ralf Meyer. 2025-06-24. Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences. https://doi.org/10.2140/om.2026.3.145

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