Operator Algebras from Graphs and Categories of Paths

Abstract: Let $G$ be a directed graph. The set of all paths in $G$ forms a semigroupoid under concatenation, and the left regular representation of this semigroupoid gives a family of partial isometries that generate an operator algebra called a free semigroupoid algebra. In this talk, I will outline this construction and discuss how it can be applied to categories of paths, which are a generalization of graphs. I will also give some examples of free semigroupoid algebras generated from categories of paths.

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