Deformations of Koszul Artin–Schelter Gorenstein algebras
Deformations of Koszul Artin–Schelter Gorenstein algebras
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DOI：
10.1007/s00229-012-0580-z
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发表时间：
2013-02
影响因子：
0.6
通讯作者：
Ji-wei He;F. van Oystaeyen;Yinhuo Zhang
中科院分区：
文献类型：
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作者：
Ji-wei He;F. van Oystaeyen;Yinhuo Zhang
我们计算了有限全局维Koszul Artin-Schelter (AS) Gorenstein代数的poincar<s:1> - birkhoff - witt (PBW)-变形的中山自同构，并给出了Koszul Calabi-Yau代数增广PBW-变形为Calabi-Yau的判据。讨论了增广pbw变形与非增广情况下的Calabi-Yau性质之间的关系。明确地给出了整体维数2和3的Koszul AS-Gorenstein代数的pbw变形的中山自同构。我们证明了如果一个梯度Calabi-Yau代数的pbw变形仍然是Calabi-Yau，那么在一些温和的条件下，它是由一个势来定义的。一些经典结果也得到了恢复。本文中使用的主要方法是基于线性代数的初等方法。本文获得的结果将应用于后续的论文（He et al.， Skew多项式代数与AS正则代数中的系数，预印本，2011）。
We compute the Nakayama automorphism of a Poincaré–Birkhoff–Witt (PBW)-deformation of a Koszul Artin–Schelter (AS) Gorenstein algebra of finite global dimension, and give a criterion for an augmented PBW-deformation of a Koszul Calabi–Yau algebra to be Calabi–Yau. The relations between the Calabi–Yau property of augmented PBW-deformations and that of non-augmented cases are discussed. The Nakayama automorphisms of PBW-deformations of Koszul AS–Gorenstein algebras of global dimensions 2 and 3 are given explicitly. We show that if a PBW-deformation of a graded Calabi–Yau algebra is still Calabi–Yau, then it is defined by a potential under some mild conditions. Some classical results are also recovered. Our main method used in this article is elementary and based on linear algebra. The results obtained in this article will be applied in a subsequent paper (He et al., Skew polynomial algebras with coefficients in AS regular algebras, preprint, 2011).