4 papers
An introduction to separated graphs and their type semigroups
Pere Ara
We introduce -algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo -algebras associated with a self-similar action…
The Leavitt inverse semigroup of a separated graph
Pere Ara, Alcides Buss, Ado Dalla Costa
We introduce and study a new inverse semigroup associated to a separated graph , which we call the \emph{Leavitt inverse semigroup}. This semigroup is obtained as a quotient…
Inverse semigroups of separated graphs and associated algebras
Pere Ara, Alcides Buss, Ado Dalla Costa
In this paper we introduce an inverse semigroup associated to a separated graph and describe its internal structure. In particular we show that it is str…
L^2-Betti numbers arising from the lamplighter group
Pere Ara, Joan Claramunt
We apply a construction developed in a previous paper by the authors in order to obtain a formula which enables us to compute -Betti numbers coming from a family of group a…