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Transformation Groups

, Volume 13, Issue 3–4, pp 855–895 | Cite as

Cluster Algebras of Finite Type via Coxeter Elements and Principal Minors

  • Shih-Wei YangEmail author
  • Andrei Zelevinsky
Article

Abstract

We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in the simply connected semisimple algebraic group of the same Cartan–Killing type. In this realization, the cluster variables appear as certain (generalized) principal minors.

Keywords

Weyl Group Simple Root Finite Type Cluster Variable Initial Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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