Pere Ara (Universitat Autònoma de Barcelona)
The inverse semigroup of a separated graph
Abstract: For a directed graph $E$, the graph semigroup $S(E)$ was defined by Ash and Hall in 1975. The graph semigroup $S(E)$ is an inverse semigroup, and has been studied by many authors in connection with the theories of graph C*-algebras, Leavitt path algebras, and topological groupoids. For a separated graph $(E,C)$, the direct analogue of $S(E)$ is not an inverse semigroup in general. However, we will introduce an inverse semigroup $IS(E,C)$ for each separated graph, which produces the same graph semigroup $S(E)$ as above in the non-separated case. We will develop a normal form of the elements of $IS(E,C)$ in close analogy to the Scheiblich normal form for elements of the free inverse semigroup.
This is joint work in progress with Alcides Buss and Ado Dalla Costa, both from Universidade Federal de Santa Catarina (Brazil).