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.
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Aslak Bakke Buan, Robert J. Marsh, Idun Reiten, Cluster mutation via quiver representations. Comment. Math. Helv. 83 (2008), no. 1, pp. 143–177DOI 10.4171/CMH/121