Classification conjectures for Leavitt path algebras

TL;DR

This survey reviews current research, conjectures, and results on the classification of Leavitt path algebras, highlighting their connections to symbolic dynamics and $C^*$-algebras.

Contribution

It compiles and discusses recent developments, open questions, and conjectures in the classification theory of Leavitt path algebras.

Findings

Summary of existing classification results

Identification of key open problems and conjectures

Overview of connections to symbolic dynamics and $C^*$-algebras

Abstract

The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and $C^*$-algebras where the major classification programs have been a domain of intense research in the last 50 years. In this survey article, we gather together current lines of research in the classification of Leavitt path algebras, questions, conjectures, and some of the results about them that have been obtained so far.