Maximal green sequences of quivers with multiple edges

Abstract

In this paper we completely describe maximal green sequences (MGS) of acyclic quivers with multiple edges in terms of maximal green sequences of their multiple edge-free (ME-free) versions. In particular we establish that any MGS of a quiver must be an ME-free MGS of its ME-free version. For quivers with oriented cycles our results for acyclic quivers do not apply. However a weaker result is available under certain conditions.