Triangulated categories of matrix factorizations for regular systems of weights with $\epsilon=-1$
Triangulated categories of matrix factorizations for regular systems of weights with $\epsilon=-1$
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DOI：
10.1016/j.aim.2008.11.001
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发表时间：
2007-08
期刊：
影响因子：
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通讯作者：
H. Kajiura;Kyoji Saito;A. Takahashi
中科院分区：
文献类型：
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作者：
H. Kajiura;Kyoji Saito;A. Takahashi
我们在多项式的分次矩阵分解的三角化范畴中构造了一个完全强例外集合，该多项式与一个最小指数等于−1的非退化正则权系统相关联。在相应的Grothendieck群中，强例外集合定义了一个符号为（1，0，2）的广义根系的根基和一个有限阶Coxeter元，其本原特征向量是关于Weyl群的IV型扩展对称域中的正则元。
We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a nondegenerate regular system of weights whose smallest exponents are equal to −1. In the associated Grothendieck group, the strongly exceptional collection defines a root basis of a generalized root system of sign (l,0,2) and a Coxeter element of finite order, whose primitive eigenvector is a regular element in the expanded symmetric domain of type IV with respect to the Weyl group.