A Survey on The Ideal Structure of Leavitt Path Algebras

TL;DR

This survey provides an overview of the ideal structures in Leavitt path algebras, focusing on the correspondence between ideals and graph-theoretic subsets, summarizing recent developments in the field.

Contribution

It offers a comprehensive overview of ideal classifications and their lattice structures in Leavitt path algebras, highlighting recent research progress.

Findings

Detailed classification of ideals in Leavitt path algebras

Correspondence between ideals and hereditary saturated subsets

Summary of recent literature on ideal structures

Abstract

There is an extensive recent literature on the graded, non-graded, prime, primitive, maximal ideals of Leavitt path algebras. In this introductory level survey, we will be giving an overview of different types of ideals and the correspondence between the lattice of ideals and the lattice of hereditary and saturated subsets of the graph over which the Leavitt path algebra is constructed.