# Inverse semigroups and Leavitt path algebras

The study of Leavitt path algebras developed from foundational work of W.G. Leavitt in the early 1960’s on the invariant basis problem for free modules over non-commutative rings, and also from work in the late 1990’s on Cuntz-Krieger graph $C^{\ast}$-algebras. In this talk I will discuss the construction of an inverse semigroup (referred to as a “Leavitt inverse semigroup”) associated with a directed graph. Leavitt inverse semigroups are homomorphic images of graph inverse semigroups: they provide some (limited) structural information and some information about the isomorphism problem for Leavitt path algebras.

This is joint work with David Milan and Zhengpan Wang.

## Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

John Meakin

## Speaker's Institution

Department of Mathematics, University of Nebraska-Lincoln, USA

## Area

Semigroups, Automata and Languages