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math.OA2026
Covariant representations of actions of inverse semigroups: a new approach to the reduced and essential crossed-product C*-algebras
Astrid an Huef, Ilija Tolich
We consider an action of an inverse semigroup on a C*-algebra and use it to construct a groupoid of germs with unit space the spectrum of . Motivated by the representation t…
math.OA2026
Topologically free non-Hausdorff groupoids
Lisa Orloff Clark, Ryan Thompson, Ilija Tolich
We study three conditions that control the behaviour of isotropy in étale groupoids, and their relationships under the additional assumptions of second-countability and Hausdorffne…
math.OA2026
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…