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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;;
Keywords: Deformation, Koszul Algebra, AS-Gorenstein algebra
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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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