19 citations · 99 across the 14 of their papers we have counts for
22 papers
Uniqueness theorems for combinatorial C*-algebras
Charles Starling
Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data…
A new uniqueness theorem for the tight C*-algebra of an inverse semigroup
Charles Starling
We prove a new uniqueness theorem for the tight C*-algebras of an inverse semigroup by generalizing the uniqueness theorem given for étale groupoid C*-algebras by Brown, Nagy, Rezn…
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…
Locally Hausdorff Tight Groupoids Generalised
Tristan Bice, Charles Starling
We extend Exel's ample tight groupoid construction to non-ample groupoids, even in the general locally Hausdorff case.
Hausdorff Tight Groupoids Generalised
Tristan Bice, Charles Starling
We extend Exel's ample tight groupoid construction to general locally compact étale groupoids in the Hausdorff case. Moreover, we show how inverse semigroups are represented in thi…
-algebras of self-similar graphs over arbitrary graphs
Ruy Exel, Enrique Pardo, Charles Starling
In this note we extend the construction of a -algebra associated to a self-similar graph to the case of arbitrary countable graphs. We reduce the problem to the row-finite cas…
Simplicity of algebras associated to non-Hausdorff groupoids
Lisa Orloff Clark, Ruy Exel, Enrique Pardo +2
We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and g…
General Non-Commutative Locally Compact Locally Hausdorff Stone Duality
Tristan Bice, Charles Starling
We extend the classical Stone duality between zero dimensional compact Hausdorff spaces and Boolean algebras. Specifically, we simultaneously remove the zero dimensionality restric…
Bratteli-Vershik models for partial actions of
Thierry Giordano, Daniel Gonçalves, Charles Starling
Let and be open subsets of the Cantor set with finite disjoint complements, and let be a homeomorphism with dense orbits. Building from the ideas of Herman, Putn…
Locally Compact Stone Duality
Tristan Bice, Charles Starling
We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattic…
C*-algebras of Boolean inverse monoids - traces and invariant means
Charles Starling
To a Boolean inverse monoid we associate a universal C*-algebra and show that it is equal to Exel's tight C*-algebra of . We then show that any invariant mean on…
Inverse semigroup shifts over countable alphabets
Daniel Gonçalves, Marcelo Sobottka, Charles Starling
In this work we characterize shift spaces over infinite countable alphabets that can be endowed with an inverse semigroup operation. We give sufficient conditions under which zero-…
Two-sided shift spaces over infinite alphabets
Daniel Gonçalves, Marcelo Sobottka, Charles Starling
Ott, Tomforde, and Willis proposed a useful compactification for one-sided shifts over infinite alphabets. Building from their idea we develop a notion of two-sided shift spaces ov…
Inverse semigroups associated to subshifts
Charles Starling
The dynamics of a one-sided subshift can be modeled by a set of partially defined bijections. From this data we define an inverse semigroup …
Sliding block codes between shift spaces over infinite alphabets
Daniel Gonçalves, Marcelo Sobottka, Charles Starling
Recently Ott, Tomforde and Willis introduced a notion of one-sided shifts over infinite alphabets and proposed a definition for sliding block codes between such shift spaces. In th…
Amenable actions of inverse semigroups
Ruy Exel, Charles Starling
We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-D…
Boundary quotients of C*-algebras of right LCM semigroups
Charles Starling
We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or interse…
Self-Similar Graph C*-Algebras and Partial Crossed Products
Ruy Exel, Charles Starling
In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to incl…
K-theory of crossed products of tiling C*-algebras by rotation groups
Charles Starling
Let be a tiling space and let be the maximal group of rotations which fixes . Then the cohomology of and are both invariants which give useful geometric inform…
Division Point Measures from Primitive Substitutions
Daniel Gonçalves, Charles Starling
In this note we extend results of Olli concerning limits of point measures arising from substitutions. We consider a general primitive substitution on a finite polygon set in $\mat…
Finite symmetry group actions on substitution tiling C*-algebras
Charles Starling
For a finite symmetry group of an aperiodic substitution tiling system $(\p,ω)$, we show that the crossed product of the tiling C*-algebra $\Aw$ by has real rank zero, trac…
The tiling C*-algebra viewed as a tight inverse semigroup algebra
Ruy Exel, Daniel Gonçalves, Charles Starling
We realize Kellendonk'?s C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the tiling, thus providing further evidence that the tight…