6 papers
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…
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…
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…
C*-algebras from partial isometric representations of LCM semigroups
Charles Starling, Ilija Tolich
We give a new construction of a C*-algebra from a cancellative semigroup via partial isometric representations, generalising the construction from the second named author's the…
HNN extensions of quasi-lattice ordered groups and their operator algebras
Astrid an Huef, Iain Raeburn, Ilija Tolich
The Baumslag-Solitar group is an example of an HNN extension. Spielberg showed that it has a natural positive cone, and that it is then a quasi-lattice ordered group in the sense o…
Structure theorems for star-commuting power partial isometries
Astrid an Huef, Iain Raeburn, Ilija Tolich
We give a new formulation and proof of a theorem of Halmos and Wallen on the structure of power partial isometries on Hilbert space. We then use this theorem to give a structure th…