Cluster mutation via quiver representations
Top Cited Papers
Open Access
- 31 March 2008
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Commentarii Mathematici Helvetici
- Vol. 83 (1) , 143-177
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 theoretic interpretation of cluster mutation in case of acyclic cluster algebras.Keywords
All Related Versions
This publication has 17 references indexed in Scilit:
- Tilting theory and cluster combinatoricsAdvances in Mathematics, 2006
- Quivers with Relations and Cluster Tilted AlgebrasAlgebras and Representation Theory, 2006
- Cluster algebras and Weil-Petersson formsDuke Mathematical Journal, 2005
- Cluster algebras III: Upper bounds and double Bruhat cellsDuke Mathematical Journal, 2005
- Generalized associahedra via quiver representationsTransactions of the American Mathematical Society, 2003
- Cluster Algebras and Poisson GeometryMoscow Mathematical Journal, 2003
- Polytopal Realizations of Generalized AssociahedraCanadian Mathematical Bulletin, 2002
- The Laurent PhenomenonAdvances in Applied Mathematics, 2002
- A characterization of hereditary categories with tilting objectInventiones Mathematicae, 2001
- Modules without self-extensions and Nakayama's conjectureArchiv der Mathematik, 1984