The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.
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For pseudo-free self-similar actions of countable groups on countable graphs with amenable vertex stabilizers, the primitive ideal space of the Exel-Pardo algebra is described graph-theoretically when the stabilizers do not contribute to the ideal structure.
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Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences
The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.
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The ideal structure of Exel-Pardo algebras and their higher rank analogues
For pseudo-free self-similar actions of countable groups on countable graphs with amenable vertex stabilizers, the primitive ideal space of the Exel-Pardo algebra is described graph-theoretically when the stabilizers do not contribute to the ideal structure.