Tame Quivers have finitely many m-Maximal Green Sequences

Kiyoshi Igusa, Ying Zhou

Published 2017-06-28Version 1

In this paper we state and prove the statement that tame quivers 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. Finally we strengthen the property of having finitely many $m$-maximal green sequences to almost morphism finiteness and prove that all path algebras of quivers of finite or tame type are almost morphism finite.