Mutation-finite quivers with real weights

Abstract

We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrisable matrix has a geometric realisation by reflections. We also explore the structure of acyclic representatives in finite mutation classes and their relations to acute-angled simplicial domains in the corresponding reflection groups.

Keywords

• 13F60
• 20H15
• 51F15