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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/22586

Title: Cleft extensions of Koszul twisted Calabi–Yau algebras
Authors: Yu, Xiaolan
Van Oystaeyen, Fred
Zhang, Yinhuo
Issue Date: 2016
Citation: ISRAEL JOURNAL OF MATHEMATICS, 214(2), p. 785-829
Abstract: Let H be a twisted Calabi–Yau (CY) Hopf algebra and σ a 2-cocycle on H. Let A be an N-Koszul twisted CY algebra such that A is a graded Hσ- module algebra. We show that the cleft extension A#σH is also a twisted CY algebra. This result has two consequences. Firstly, the smash product of an N-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects of U(D, λ), a class of pointed Hopf algebras introduced by Andruskiewitsch and Schneider, are Calabi–Yau algebras.
URI: http://hdl.handle.net/1942/22586
DOI: 10.1007/s11856-016-1362-1
ISI #: 000382866000012
ISSN: 0021-2172
Category: A1
Type: Journal Contribution
Validation: ecoom, 2017
Appears in Collections: Research publications

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