Maximal green sequences for string algebras

TL;DR

This paper investigates the existence and finiteness of maximal green sequences in string algebras, providing conditions that guarantee their presence and finiteness, with implications across representation theory and related fields.

Contribution

It offers new sufficient conditions for string algebras to admit finitely many maximal green sequences, advancing understanding in algebraic and combinatorial structures.

Findings

Identifies conditions ensuring existence of maximal green sequences

Establishes criteria for finiteness of such sequences in string algebras

Enhances theoretical framework connecting string algebras and cluster theory

Abstract

Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. The two fundamental questions about maximal green sequences are whether a given algebra admits such sequences and, if so, does it admit only finitely many. We study maximal green sequences in the case of string algebras and give sufficient conditions on the algebra that ensure an affirmative answer to these questions.