Cluster mutation via quiver representations

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.

28 pages, a new Section 2 to correct an error in earlier version

References in corpus (4)

• On triangulated orbit categories
• Tilting theory and cluster combinatorics
• Cluster algebras: notes for 2004 IMCC (Chonju, Korea, August 2004)
• Cluster algebras associated with extended Dynkin quivers

Cited by in corpus (8)

• Cluster Complexes via Semi-Invariants
• Quivers with potentials and their representations I: Mutations
• From triangulated categories to cluster algebras
• On cluster algebras with coefficients and 2-Calabi-Yau categories
• The cluster category of a canonical algebra
• An approach to non simply laced cluster algebras
• Representation Dimension of Cluster Concealed Algebras
• On tilting modules over cluster-tilted algebras