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.
Operator Algebras from Graphs and Categories of Paths
Juliana Bukoski, Georgetown College
2022 AWM Research Symposium
New EDGE (Enhancing Diversity in Graduate Education) PhDs Special Session: Pure and Applied talks by Women Math Warriors