Ample Group Action on AS-regular Algebras and Noncommutative Graded Isolated Singularities
Ample Group Action on AS-regular Algebras and Noncommutative Graded Isolated Singularities
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DOI：
10.1090/tran/6580
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
I. Mori;Kenta Ueyama
中科院分区：
文献类型：
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作者：
I. Mori;Kenta Ueyama
本文在右Notherian分次代数$A$上引入了群作用$G$的幅值概念，并证明了它与本文第二作者引入的分次孤立奇点的概念密切相关.此外，如果$S$是Noether As-正则代数，$G$是作用于$S$上的有限取值群，则我们将证明${数学D}^b(操作名{尾}S^G)\从D}^b(操作名{mod}S*G)$其中$S$是$S$的Beilinson代数.我们还将显式地计算一个箭图$Q_{S，G}$，使得当$S$是2维时，${\数学D}^b(运算器名{尾}S^G)\从{\数学D}^b(\运算器名{mod}KQ_{S，G})$。
In this paper, we introduce a notion of ampleness of a group action $G$ on a right noetherian graded algebra $A$, and show that it is strongly related to the notion of $A^G$ to be a graded isolated singularity introduced by the second author of this paper. Moreover, if $S$ is a noetherian AS-regular algebra and $G$ is a finite ample group acting on $S$, then we will show that ${\mathcal D}^b(\operatorname{tails} S^G)\cong {\cal D}^b(\operatorname{mod} \nabla S*G)$ where $\nabla S$ is the Beilinson algebra of $S$. We will also explicitly calculate a quiver $Q_{S, G}$ such that ${\mathcal D}^b(\operatorname{tails} S^G)\cong {\mathcal D}^b(\operatorname{mod} kQ_{S, G})$ when $S$ is of dimension 2.