Categorification of Acyclic Cluster Algebras: An Introduction

  • Bernhard KellerEmail author
Part of the Progress in Mathematics book series (PM, volume 287)


This is a concise introduction to Fomin–Zelevinsky’s cluster algebras and their links with the representation theory of quivers in the acyclic case. We review the definition cluster algebras (geometric, without coefficients), construct the cluster category and present the bijection between cluster variables and rigid indecomposable objects of the cluster category.

Key words

Cluster algebra Associahedron Quiver representation Triangulated category Hallalgebra 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUMR 7586 du CNRS, Université Paris 7-Denis DiderotParis Cedex 05France

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