Tame Hereditary Algebras have finitely many m-Maximal Green Sequences

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.