Deformations of Koszul Artin–Schelter Gorenstein algebras
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- 作者：Ji-Wei He (1) (2)
Fred Van Oystaeyen (2)
Yinhuo Zhang (3) - 关键词：16E65 ; 15A63 ; 16S37
- 刊名：manuscripta mathematica
- 出版年：2013
- 出版时间：4 - July 2013
- 年：2013
- 卷：141
- 期：3
- 页码：463-483
- 全文大小：259KB
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Fred Van Oystaeyen (2)
Yinhuo Zhang (3)
1. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, 312000, Zhejiang, China
2. Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020, Antwerp, Belgium
3. Department WNI, University of Hasselt, Universitaire Campus, 3590, Diepenbeek, Belgium - ISSN：1432-1785
文摘
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).