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Title: | Deformations of Koszul Artin–Schelter Gorenstein algebras | Authors: | He, Jiwei Van Oystaeyen, Fred ZHANG, Yinhuo |
Issue Date: | 2013 | Source: | Manuscript Mathematica, 141 (3-4), p. 463-483 | Abstract: | We compute the Nakayama automorphism of a Poincare-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). | Notes: | Reprint Address: He, JW (reprint author) - Shaoxing Coll Arts & Sci, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China. E-mail Addresses:jwhe@usx.edu.cn; fred.vanoystaeyen@ua.ac.be; yinhuo.zhang@uhasselt.be | Keywords: | Deformation, Koszul Algebra, AS-Gorenstein algebra | Document URI: | http://hdl.handle.net/1942/15242 | Link to publication/dataset: | http://link.springer.com/content/pdf/10.1007%2Fs00229-012-0580-z.pdf | ISSN: | 0025-2611 | e-ISSN: | 1432-1785 | DOI: | 10.1007/s00229-012-0580-z | ISI #: | 000319914800005 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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