10 papers
Notes on universal C*-algebras
Gilles G. de Castro
In these notes, we explain in details the construction of the universal C*-algebra as done by Blackadar, starting with the construction of the free *-algebra. At the end, we explai…
Graph morphisms as groupoid actors
Gilles G. de Castro, Ralf Meyer
We describe proper actors from the underlying groupoid of a graph C*-algebra to another étale groupoid in terms of bisections. This allows to understand graph morphisms and the *-h…
Boundary path groupoids of generalized Boolean dynamical systems and their C*-algebras
Gilles G. de Castro, Eun Ji Kang
In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system . For the first groupoid, we…
Leavitt path algebras of labelled graphs
Giuliano Boava, Gilles G. de Castro, Daniel Gonçalves +1
A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as wel…
Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems
Gilles G. de Castro, Daniel Gonçalves, Daniel W. van Wyk
An ultragraph gives rise to a labelled graph with some particular properties. In this paper we describe the algebras associated to such labelled graphs as groupoid algebras. More p…
Infinite sum relations on universal C*-algebras
Giuliano Boava, Gilles G. de Castro
We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular…
Coverages on Inverse Semigroups
Gilles G. de Castro
First we give a definition of a coverage on a inverse semigroup that is weaker than the one gave by a Lawson and Lenz and that generalizes the definition of a coverage on a semilat…
Labelled space -algebras as partial crossed products and a simplicity characterization
Gilles G. de Castro, Daniel W. van Wyk
A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space -algebras are isomorphic. An improved charac…
Groupoid models for the C*-algebra of labelled spaces
Giuliano Boava, Gilles G. de Castro, Fernando de L. Mortari
We define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. We then define…
Recovering the boundary path space of a topological graph using pointless topology
Gilles G. de Castro
First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $…