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arXiv · 0804.3303

Cluster algebras of finite type via Coxeter elements and principal minors

Shih-Wei Yang·Andrei Zelevinsky
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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.

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Shih-Wei Yang, Andrei Zelevinsky. 2008-05-19. Cluster algebras of finite type via Coxeter elements and principal minors. https://arxiv.org/abs/0804.3303

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