10 citations · 27 across the 9 of their papers we have counts for
11 papers
C*-Algebras of one-sided subshifts over arbitrary alphabets
Giuliano Boava, Gilles G. de Castro, Daniel Gonçalves +1
We associate a C*-algebra with a subshift over an arbitrary, possibly infinite, alphabet. We show that …
Étale categories, restriction semigroups, and their operator algebras
Natã Machado, Gilles G. de Castro
We define the full and reduced non-self-adjoint operator algebras associated with étale categories and restriction semigroups, answering a question posed by Kudryavtseva and Lawson…
Algebras of one-sided subshifts over arbitrary alphabets
Giuliano Boava, Gilles G. de Castro, Daniel Gonçalves +1
We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy b…
Reconstruction of twisted Steinberg algebras
Becky Armstrong, Gilles G. de Castro, Lisa Orloff Clark +6
We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra. We identify precisely whic…
Haar systems, KMS states on von Neumann algebras and -algebras on dynamically defined groupoids and Noncommutative Integration
Gilles G. de Castro, Artur O. Lopes, Gabriel Mantovani
We analyse certain Haar systems associated to groupoids obtained by certain natural equivalence relations of dynamical nature on sets like , $\{1,2,...,d\…
KMS and ground states on ultragraph C*-algebras
Gilles Gonçalves de Castro, Daniel Gonçalves
We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. We focus on ultragraphs that satisfy Condition~(RFUM), so that we can use the p…
C*-algebras of labelled spaces and their diagonal C*-subalgebras
Giuliano Boava, Gilles G. de Castro, Fernando de L. Mortari
Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We constr…
Inverse semigroups associated with labelled spaces and their tight spectra
Giuliano Boava, Gilles de Castro, Fernando de L. Mortari
The notion of a labelled space was introduced by Bates and Pask in generalizing certain classes of C*-algebras. Motivated by Exel's work on inverse semigroups and combinatorial C*-…
KMS states for the generalized gauge action on graph algebras
Gilles de Castro, Fernando Mortari
Given a positive function on the set of edges of an arbitrary directed graph , we define a one-parameter group of automorphisms on the C*-algebra of the graph …
KMS States, Entropy and a Variational Principle for Pressure
Gilles G. de Castro, Artur O. Lopes
We want to relate the concepts of entropy and pressure to that of KMS states for -Algebras. Several different definitions of entropy are known in our days. The one we describe…
C*-Algebras Associated with Iterated Function Systems
Gilles G. de Castro
We review Kajiwara and Watatani's construction of a C*-algebra from an iterated function system (IFS). If the IFS satisfies the finite branch condition or the open set condition, w…