Cluster mutation via quiver representations

Preprint

8 September 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0412077

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.

Keywords

QUIVER REPRESENTATIONS
REPRESENTATIONS MATRIX
CLUSTER MUTATION
CLUSTER ALGEBRAS
MATRIX MUTATION

All Related Versions

Version 1, 2004-12-03, ArXiv
Version 2, 2005-09-08, ArXiv

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