Infinite string bricks and Sturmian words over some gentle algebras

TL;DR

This paper classifies infinite string modules over gentle algebras, linking them to Sturmian words, and extends these results to broader classes of gentle algebras.

Contribution

It provides a complete classification of infinite string modules over the double-Kronecker gentle algebra and establishes a bijection with Sturmian words, extending to larger gentle algebras.

Findings

Classification of infinite string modules over double-Kronecker gentle algebra

Bijection between modules and Sturmian words

Extension of results to larger gentle algebras

Abstract

We study infinite string modules that are bricks over some gentle algebras. In particular, we first give a complete classification of these modules over the double-Kronecker gentle algebra and prove that each family is in bijection with a family of Sturmian (binary) words. We then generalize some of our results to a larger family of gentle algebras.