Cluster algebras of finite type via coxeter elements and principal minors

Shih-Wei Yang, Andrei Zelevinsky

Research output: Contribution to journalArticle

33 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)855-895
Number of pages41
JournalTransformation Groups
Volume13
Issue number3-4
DOIs
Publication statusPublished - 2008 Dec 1

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Cluster Algebra
Finite Type
Minor
Semisimple Groups
Arbitrary
Algebraic Groups
Ring
Algebra
Cell
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Yang, Shih-Wei ; Zelevinsky, Andrei. / Cluster algebras of finite type via coxeter elements and principal minors. In: Transformation Groups. 2008 ; Vol. 13, No. 3-4. pp. 855-895.
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Cluster algebras of finite type via coxeter elements and principal minors. / Yang, Shih-Wei; Zelevinsky, Andrei.

In: Transformation Groups, Vol. 13, No. 3-4, 01.12.2008, p. 855-895.

Research output: Contribution to journalArticle

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