Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras

JOURNAL OF ALGEBRA

卷:390

Article

He, Ji-Wei^1,2  Van Oystaeyen, Fred²  Zhang, Yinhuo³ 

[1] Shaoxing Coll Arts & Sci, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China

[2] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium

[3] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium

关键词: Koszul Artin-Schelter regular algebra;    Skew polynomial algebra;    Calabi-Yau algebra;    Superpotential;    PBW-deformation;   

DOI  :  10.1016/j.jalgebra.2013.05.023

来源: Elsevier

【 摘 要 】

Let A be a Koszul Artin-Schelter regular algebra with Nakayama automorphism xi. We show that the Yoneda Ext-algebra of the skew polynomial algebra A[z; xi] is a trivial extension of a Frobenius algebra. Then we prove that A[z; xi] is Calabi-Yau; and hence each Koszul Artin-Schelter regular algebra is a subalgebra of a Koszul Calabi-Yau algebra. A superpotential (w) over cap is also constructed so that the Calabi-Yau algebra A[z; xi] is isomorphic to the derivation quotient of (w) over cap. The Calabi-Yau property of a skew polynomial algebra with coefficients in a PBW-deformation of a Koszul Artin-Schelter regular algebra is also discussed. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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