Cluster algebras of finite type via Coxeter elements and principal minors
Rings and Algebras
2008-05-19 v2 Representation Theory
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
Cite
@article{arxiv.0804.3303,
title = {Cluster algebras of finite type via Coxeter elements and principal minors},
author = {Shih-Wei Yang and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:0804.3303},
year = {2008}
}
Comments
38 pages, 2 figures; v2: minor editorial changes, to appear in Transformation Groups