Title
Deformations of Koszul Artin-Schelter Gorenstein algebras Deformations of Koszul Artin-Schelter Gorenstein algebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Berlin ,
Subject
Mathematics
Source (journal)
Manuscripta mathematica. - Berlin
Volume/pages
141(2013) :3-4 , p. 463-483
ISSN
0025-2611
ISI
000319914800005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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).
E-info
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