Commentarii Mathematici Helvetici

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Volume 83, Issue 1, 2008, pp. 143–177
DOI: 10.4171/CMH/121

Published online: 2008-03-31

Cluster mutation via quiver representations

Aslak Bakke Buan[1], Robert J. Marsh[2] and Idun Reiten[3]

(1) University of Trondheim, Norway
(2) University of Leeds, United Kingdom
(3) 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.

Keywords: Cluster algebras, cluster categories, tilting theory

Buan Aslak Bakke, Marsh Robert, Reiten Idun: Cluster mutation via quiver representations. Comment. Math. Helv. 83 (2008), 143-177. doi: 10.4171/CMH/121