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 | Source: | 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. | Keywords: | Cleft extension; Calabi-Yau algebra; Hopf algebra | Document URI: | http://hdl.handle.net/1942/22586 | ISSN: | 0021-2172 | e-ISSN: | 1565-8511 | DOI: | 10.1007/s11856-016-1362-1 | ISI #: | 000382866000012 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2017 |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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Cleft extensions of Koszul twisted Calabi-Yau algebras.pdf Restricted Access | Published version | 472.72 kB | Adobe PDF | View/Open Request a copy |
extension7.pdf | Peer-reviewed author version | 487.33 kB | Adobe PDF | View/Open |
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