Maximal green sequences of quivers with multiple edges

TL;DR

This paper characterizes maximal green sequences of acyclic quivers with multiple edges by relating them to sequences of their ME-free versions, providing a complete description and establishing necessary conditions.

Contribution

It introduces a comprehensive method to describe MGS of quivers with multiple edges via their ME-free counterparts, extending understanding of quiver mutation sequences.

Findings

MGS of acyclic quivers with multiple edges are fully described by their ME-free versions.

Any MGS of such a quiver must be an ME-free MGS of its ME-free version.

Results do not directly apply to quivers with oriented cycles, but partial results are available.

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.