Tame Hereditary Algebras have finitely many m-Maximal Green Sequences

TL;DR

This paper proves that tame hereditary algebras possess a finite number of m-maximal green sequences, extending existing results from tame quivers to a broader class of mutation sequences.

Contribution

It establishes the finiteness of m-maximal green sequences for tame hereditary algebras and extends the result to partially red mutation sequences.

Findings

Tame hereditary algebras have finitely many m-maximal green sequences.

The finiteness result extends to partially red mutation sequences.

The proof generalizes previous arguments used for tame quivers.

Abstract

In this paper we state and prove the statement that tame hereditary algebras have finitely many m-maximal green sequences using a generalized version of Br\"ustle-Dupont-P\'erotin's argument that tame quivers have finitely many maximal green sequences. Then we extend this theorem to mutation sequences which are partially red.