Subquivers of mutation-acyclic quivers are mutation-acyclic

2011/02/16 by Warkentin, Matthias
#05E10 (Primary) #13F60 #16G20 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1102.3382

Abstract

Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is mutation-equivalent to an acyclic quiver. This note gives a proof that full subquivers of mutation-acyclic quivers are mutation-acyclic.

Related

• Every finite acyclic quiver is a full subquiver of a quiver mutation equivalent to a bipartite quiver
• Mutation-acyclic quivers are totally proper
• Cluster mutation via quiver representations
• Cluster algebras associated with extended Dynkin quivers
• A topology on the poset of quiver mutation classes