Cluster mutation via quiver representations

  • Aslak Bakke Buan

    University of Trondheim, Norway
  • Bethany R. Marsh

    University of Leeds, United Kingdom
  • Idun Reiten

    University of Trondheim, Norway


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 theoretic interpretation of cluster mutation in case of acyclic cluster algebras.

Cite this article

Aslak Bakke Buan, Bethany R. Marsh, Idun Reiten, Cluster mutation via quiver representations. Comment. Math. Helv. 83 (2008), no. 1, pp. 143–177

DOI 10.4171/CMH/121