Title
Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Journal of algebra. - New York, N.Y.
Volume/pages
390(2013) , p. 231-249
ISSN
0021-8693
ISI
000321798700013
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
E-info
https://repository.uantwerpen.be/docman/iruaauth/48293d/0545328.pdf
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