Twisted Segre products
Twisted Segre products
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DOI：
10.1016/j.jalgebra.2022.08.017
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发表时间：
2021-11
影响因子：
0.9
通讯作者：
Ji-wei He;Kenta Ueyama
中科院分区：
文献类型：
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作者：
Ji-wei He;Kenta Ueyama
我们引入了Z-分次代数A和B关于扭曲映射∘ψ的扭曲Segre积A和B的概念。证明了：如果A和B是Noether Koszul Artin-Schelter正则代数，且ψ是一个扭曲映射，使得扭曲Segre积A∘ψB是Noether的，则A∘ψB是非交换分次孤立奇点.为了证明这一结果，引入了稠密(双)分次代数的概念。此外，我们还证明了A=k[u，v]和B=k[x，y]关于对角扭曲映射∘ψ的扭曲段积A-ψB是非对易二次曲面(特别是Noether曲面)，并计算了它上的分次极大Cohen-Macaulay模的稳定范畴。
We introduce the notion of the twisted Segre product A∘ ψ B of Z-graded algebras A and B with respect to a twisting map ψ. It is proved that if A and B are noetherian Koszul Artin-Schelter regular algebras and ψ is a twisting map such that the twisted Segre product A∘ ψ B is noetherian, then A∘ ψ B is a noncommutative graded isolated singularity. To prove this result, the notion of densely (bi-) graded algebras is introduced. Moreover, we show that the twisted Segre product A∘ ψ B of A= k [u, v] and B= k [x, y] with respect to a diagonal twisting map ψ is a noncommutative quadric surface (so in particular it is noetherian), and we compute the stable category of graded maximal Cohen-Macaulay modules over it.