Publication
Title
Deformations of Koszul Artin-Schelter Gorenstein algebras
Author
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).
Language
English
Source (journal)
Manuscripta mathematica. - Berlin
Publication
Berlin : 2013
ISSN
0025-2611
Volume/pages
141:3-4(2013), p. 463-483
ISI
000319914800005
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 04.09.2013
Last edited 11.07.2017
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