Categorification of Skew-symmetrizable Cluster Algebras
Categorification of Skew-symmetrizable Cluster Algebras
复制标题
DOI：
10.1007/s10468-010-9228-4
复制
发表时间：
2009-09
影响因子：
0.6
通讯作者：
Laurent Demonet
中科院分区：
文献类型：
--
作者：
Laurent Demonet
我们提出了一个新的分类斜对称化簇代数的框架。从一个被赋予有限群Γ作用的精确稳定的2-Calabi-Yau范畴出发，在的极大刚性Γ不变对象集上构造了一个Γ等变突变。使用适当的簇特征，我们可以将这些数据链接到显式的斜对称化的簇代数。作为应用，我们证明了在这种情况下簇单项式的线性无关性。最后，我们用与部分旗簇和Kac-Moody群的酉子群相关的例子来说明我们的构造，推广到非简单花边的情形，推广了Geiü-Leclerc-Schröer的几个结果。
We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi–Yau categoryendowed with the action of a finite group Γ, we construct a Γ-equivariant mutation on the set of maximal rigid Γ-invariant objects of. Using an appropriate cluster character, we can then link these date to an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac–Moody groups, generalizing to the non simply-laced case several results of Geiß–Leclerc–Schröer.