Graded maximal Cohen–Macaulay modules over noncommutative graded Gorenstein isolated singularities
Graded maximal Cohen–Macaulay modules over noncommutative graded Gorenstein isolated singularities
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DOI：
10.1016/j.jalgebra.2013.02.022
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发表时间：
2013-06
影响因子：
0.9
通讯作者：
Kenta Ueyama
中科院分区：
文献类型：
--
作者：
Kenta Ueyama
在本文中，我们定义了非交换分级孤立奇点的概念，并研究了 AS-Gorenstein 孤立奇点及其分级最大 Cohen-Macaulay 模的类别。特别是，对于维度 d⩾2 的 AS-Gorenstein 代数 A，我们证明 A 是分级孤立奇点当且仅当 A 上分级最大 Cohen-Macaulay 模的稳定范畴具有 Serre 函子。利用这个结果，我们还证明了某些 AS-正则代数的维罗内斯子代数上的分级最大 Cohen-Macaulay 模类别中簇倾斜对象的存在。
In this paper, we define a notion of noncommutative graded isolated singularity, and study AS-Gorenstein isolated singularities and the categories of graded maximal Cohen–Macaulay modules over them. In particular, for an AS-Gorenstein algebra A of dimension d⩾2, we show that A is a graded isolated singularity if and only if the stable category of graded maximal Cohen–Macaulay modules over A has the Serre functor. Using this result, we also show the existence of cluster tilting objects in the categories of graded maximal Cohen–Macaulay modules over Veronese subalgebras of certain AS-regular algebras.