Cluster Algebras of Finite Type via Coxeter Elements and Principal Minors
Cluster Algebras of Finite Type via Coxeter Elements and Principal Minors
复制标题
通过 Coxeter 元素和主次数的有限型簇代数
DOI：
10.1007/s00031-008-9025-x
复制
发表时间：
2008
影响因子：
0.7
通讯作者：
A. Zelevinsky
中科院分区：
文献类型：
--
作者：
Shihai Yang;A. Zelevinsky
给出了在任意非循环种子上具有主系数的任意有限型簇代数的一致几何实现。该代数被实现为同一Cartan-Killing型单连通半单代数群中某一约简双Bruhat胞格的坐标环。在这种实现中，簇变量表现为某些(广义)主子式。
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.