On the quasitriangular structures of abelian extensions of ℤ2. Issue 11 (3rd November 2021)

• Record Type: Journal Article
• Authors: Zhou, Kun; Liu, Gongxiang
• Is Part Of: Communications in algebra. Volume 49:Issue 11(2021)
• Page Start: 4755
• Page End: 4762
• Publication Date: 2021-11-03
• Subjects: Abelian extension -- quasitriangular Hopf algebra; 16T05 (primary) -- 16T25 (secondary); Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1929274
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras k G # σ, τ k Z 2 constructed through abelian extensions of k Z 2 by k G for an abelian group G . We prove that there are only two forms of them and we get a complete list of all universal R -matrices of the generalized Kac-Paljutkin algebra H 2 n 2 (see Section 2 for the definition).