Universitat Autònoma de Barcelona, España
A separated graph is a pair (E, C), where E is a directed graph, C=⊔v∈E0 Cv , and Cv is a partition of s−1(v) (into pairwise disjoint nonempty subsets) for every vertex v. For each separated graph (E, C), we will introduce its inverse semigroup S(E, C) and we will give a normal form for its elements. We will relate this inverse semigroup with some tame algebras associated to (E, C), such as the tame Cohn path algebra Cab(E, C) and the tame Leavitt path algebra Lab(E, C). Corresponding C*-algebras will also be considered.
This is joint work in progress with Alcides Buss and Ado Dalla Costa, both from Universidade Federal de Santa Catarina.