Monoids, dynamics and Leavitt path algebras

TL;DR

This paper explores the rich structure of Leavitt path algebras, highlighting their connections to various mathematical fields such as dynamics, operator algebras, and non-commutative geometry, and discusses their underlying monoid structures.

Contribution

It provides a comprehensive overview of the interplay between monoids, dynamics, and Leavitt path algebras, emphasizing new insights into their algebraic and dynamical properties.

Findings

Leavitt path algebras relate to symbolic dynamics and operator algebras.

The paper uncovers structural properties linking monoids and algebraic dynamics.

Connections to non-commutative geometry and representation theory are elucidated.

Abstract

Leavitt path algebras, which are algebras associated to directed graphs, were first introduced about 20 years ago. They have strong connections to such topics as symbolic dynamics, operator algebras, non-commutative geometry, representation theory, and even chip firing. In this article we invite the reader to sneak a peek at these fascinating algebras and their interplay with several seemingly disparate parts of mathematics.