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A dichotomy for inverse-semigroup crossed products via dynamical Cuntz semigroups
Becky Armstrong, Lisa Orloff Clark, Astrid an Huef +2
We characterise stable finiteness and pure infiniteness of the essential crossed product of a C*-algebra by an action of an inverse semigroup. Under additional assumptions, we prov…
Algebraic singular functions are not always dense in the ideal of -singular functions
Diego Martínez, Nóra Szakács
We give the first examples of étale (non-Hausdorff) groupoids whose -algebras contain singular elements that cannot be approximated by singular elements in $\math…
Essential groupoid amenability and nuclearity of groupoid C*-algebras
Alcides Buss, Diego Martínez
We give an alternative construction of the essential -algebra of an étale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity o…
Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids
Alcides Buss, Diego Martínez
In this paper we study the nuclearity and weak containment property of reduced cross-sectional C*-algebras of Fell bundles over inverse semigroups. In order to develop the theory,…