Subquivers of mutation-acyclic quivers are mutation-acyclic

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

paper · pdf · doi:10.48550/arxiv.1102.3382

v2: main result was found to be already known, introduction changed correspondingly

arxiv created 2011/02/18 · arxiv updated 2011/02/21

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