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Linear independence of cluster monomials for skew-symmetric cluster algebras

Part of: Arithmetic rings and other special rings Abelian categories

Published online by Cambridge University Press:  28 August 2013

Giovanni Cerulli Irelli ,
Bernhard Keller ,
Daniel Labardini-Fragoso  and
Pierre-Guy Plamondon
Giovanni Cerulli Irelli
Affiliation:
Mathematisches Institut, Universität Bonn, D-53115 Bonn, Germany email [email protected]
Bernhard Keller
Affiliation:
Université Paris Diderot - Paris 7, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France email [email protected]
Daniel Labardini-Fragoso
Affiliation:
Mathematisches Institut, Universität Bonn, D-53115 Bonn, Germany email [email protected]
Pierre-Guy Plamondon
Affiliation:
Laboratoire LMNO, Équipe Algèbre, Géométrie et Logique, Université de Caen, F14032 Caen Cedex, France email [email protected]
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Abstract

Fomin–Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all skew-symmetric cluster algebras.

Keywords

cluster algebrascluster categoriescluster monomials

MSC classification

Secondary: 18E30: Derived categories, triangulated categories 13F60: Cluster algebras
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 10 , October 2013 , pp. 1753 - 1764
Copyright
© The Author(s) 2013 

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