Cluster algebras of finite type via coxeter elements and principal minors

Shih Wei Yang, Andrei Zelevinsky

Research output: Contribution to journalArticle

35 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)855-895
Number of pages41
JournalTransformation Groups
Issue number3-4
Publication statusPublished - 2008 Dec 1


All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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