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Cluster mutation via quiver representations

Aslak Bakke Buan·Bethany Marsh·Idun Reiten
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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.

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Aslak Bakke Buan, Bethany Marsh, Idun Reiten. 2004-12-03. Cluster mutation via quiver representations. https://arxiv.org/abs/math/0412077

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