A characterization of torsion theories in the cluster category of Dynkin type A_{\infty}

TL;DR

This paper characterizes torsion theories in the cluster category of Dynkin type A_infinity by establishing a bijection with specific arc configurations, enhancing understanding of the category's structure.

Contribution

It introduces a novel bijection between torsion theories and arc configurations in the cluster category of Dynkin type A_infinity.

Findings

Bijection between torsion theories and arc configurations

New combinatorial description of torsion theories

Enhanced understanding of the structure of the cluster category

Abstract

Let D be the cluster category of Dynkin type A_{\infty}. This paper provides a bijection between torsion theories in D and certain configurations of arcs connecting non-neighbouring integers.