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Title of Journal: manuscripta math

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Abbravation: Manuscripta Mathematica

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Springer-Verlag

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10.1002/lipi.19350420304

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1432-1785

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Deformations of Koszul Artin–Schelter Gorenstein a

Authors: JiWei He Fred Van Oystaeyen Yinhuo Zhang
Publish Date: 2012/08/07
Volume: 141, Issue: 3-4, Pages: 463-483
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Abstract

We compute the Nakayama automorphism of a Poincaré–Birkhoff–Witt PBWdeformation of a Koszul Artin–Schelter AS Gorenstein algebra of finite global dimension and give a criterion for an augmented PBWdeformation of a Koszul Calabi–Yau algebra to be Calabi–Yau The relations between the Calabi–Yau property of augmented PBWdeformations and that of nonaugmented cases are discussed The Nakayama automorphisms of PBWdeformations of Koszul AS–Gorenstein algebras of global dimensions 2 and 3 are given explicitly We show that if a PBWdeformation 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

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