Cluster tilting modules and noncommutative projective schemes
Cluster tilting modules and noncommutative projective schemes
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DOI：
10.2140/pjm.2017.289.449
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发表时间：
2016-04
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影响因子：
--
通讯作者：
Kenta Ueyama
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文献类型：
--
作者：
Kenta Ueyama
本文研究了非交换投射格式与簇倾斜模的等价关系。特别地，我们证明了以下结果。设$A$是一个维数为$d\geq 2$的AS-Gorenstein代数，${\mathsf{tails}\，} A$是与$A$相关联的非交换投射概型.如果$\operatorname{gldim}（{\mathsf{tails}\，} A）< \infty$和$A$有一个$（d-1）$-簇倾斜模$X$满足其分次自同态代数是$\mathbb N$-分次的，则$X$的基本$（d-1）$-簇倾斜子模的分次自同态代数$B$是$B_0$上的双边Noether $\mathbb N$-分次AS-正则代数全局维度$d$，使得${\mathsf{tails}\，} B$等价于${\mathsf{tails}\，} A$。
In this paper, we study the relationship between equivalences of noncommutative projective schemes and cluster tilting modules. In particular, we prove the following result. Let $A$ be an AS-Gorenstein algebra of dimension $d\geq 2$ and ${\mathsf{tails}\,} A$ the noncommutative projective scheme associated to $A$. If $\operatorname{gldim}({\mathsf{tails}\,} A)< \infty$ and $A$ has a $(d-1)$-cluster tilting module $X$ satisfying that its graded endomorphism algebra is $\mathbb N$-graded, then the graded endomorphism algebra $B$ of a basic $(d-1)$-cluster tilting submodule of $X$ is a two-sided noetherian $\mathbb N$-graded AS-regular algebra over $B_0$ of global dimension $d$ such that ${\mathsf{tails}\,} B$ is equivalent to ${\mathsf{tails}\,} A$.