Cluster mutation via quiver representations

2004/12/03 by Buan, Aslak Bakke, Marsh, Bethany, Reiten, Idun · 1 citation
#05E99 (Secondary) #16G20 #16G70 (Primary) 13A99 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math/0412077

Abstract

Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we obtain a representation theoretical interpretation of cluster mutation in case of acyclic cluster algebras of finite type.

Cited by

• Examples of tilting-discrete symmetric algebras

Related

• Graded mutation in cluster categories coming from hereditary categories with a tilting object
• Subquivers of mutation-acyclic quivers are mutation-acyclic
• Cluster algebras, quiver representations and triangulated categories
• Mutation classes of finite type cluster algebras with principal coefficients
• Three kinds of mutation