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Commentarii Mathematici Helvetici

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Cluster mutation via quiver representations

Aslak Bakke Buan (1), Robert J. Marsh (2) and Idun Reiten (3)

(1) Department of Mathematical Sciences, University of Trondheim, Alfred Getz vei 1, NO-7491, TRONDHEIM, NORWAY
(2) Department of Pure Mathematics, University of Leeds, LS2 9JT, LEEDS, UNITED KINGDOM
(3) Department of Mathematical Sciences, University of Trondheim, Alfred Getz vei 1, NO-7491, 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