# The ideal intersection property for essential groupoid C*-algebras

@inproceedings{Kennedy2021TheII, title={The ideal intersection property for essential groupoid C*-algebras}, author={Matthew Kennedy and Se-Jin Kim and Xin Li and Sven Raum and Dan Ursu}, year={2021} }

We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C∗-algebra has the ideal intersection property, assuming that the groupoid is either Hausdorff or σ-compact. This leads directly to a characterisation of the simplicity of this C∗-algebra which, for Hausdorff groupoids, agrees with the reduced groupoid C∗-algebra. Specifically, we prove that the ideal intersection property is equivalent to the absence of…

## 3 Citations

Boundary maps and covariant representations

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We extend applications of Furstenberg boundary theory to the study of C∗-algebras associated to minimal actions ΓyX of discrete groups Γ on locally compact spaces X. We introduce boundary maps on (Γ,…

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. We study C ∗ -irreducibility of inclusions of reduced twisted group C ∗ -algebras and of reduced group C ∗ -algebras. We characterize C ∗ -irreducibility in the case of an inclusion arising from a…

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