We obtain the necessary and sufficient conditions for Radford＇s biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given.
In this paper, we construct a new example of Hopf group coalgebras by con- sidering Radford＇s biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radf...In this paper, we construct a new example of Hopf group coalgebras by con- sidering Radford＇s biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radford＇s biproduct Hopf algebra to admit quasitriangulax structures in the sense of Turaev group coalgebras.展开更多
Let （H,β） be a Hom-bialgebra such that β^2 = idH. （A, αA） is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category H^HYD and （B, αB） is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category...Let （H,β） be a Hom-bialgebra such that β^2 = idH. （A, αA） is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category H^HYD and （B, αB） is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YDH^H. The authors define the two-sided smash product Hom-algebra （A H B, αA β αB） and the two-sided smash coproduct Hom- coalgebra （A H B, αA β αB）. Then the necessary and sufficient conditions for （A H B, αA β αB） and （A H B, αA β αB） to be a Hom-bialgebra （called the double biproduct Hom-bialgebra and denoted by （A H B, αA β αB）） are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra （A H B, αA β） to be quasitriangular are given.展开更多
基金Supported by the NNSF of China (10871042)the NSF of Jiangsu Province (BK2009258)+1 种基金NSF of Henan Province (102300410049, 2010A110009)the Foster Foundation of Henan Normal University (2010PL01)
文摘We obtain the necessary and sufficient conditions for Radford＇s biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given.
文摘In this paper, we construct a new example of Hopf group coalgebras by con- sidering Radford＇s biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radford＇s biproduct Hopf algebra to admit quasitriangulax structures in the sense of Turaev group coalgebras.
基金supported by the Henan Provincial Natural Science Foundation of China(No.17A110007)the Foundation for Young Key Teacher by Henan Province(No.2015GGJS-088)
文摘Let （H,β） be a Hom-bialgebra such that β^2 = idH. （A, αA） is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category H^HYD and （B, αB） is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YDH^H. The authors define the two-sided smash product Hom-algebra （A H B, αA β αB） and the two-sided smash coproduct Hom- coalgebra （A H B, αA β αB）. Then the necessary and sufficient conditions for （A H B, αA β αB） and （A H B, αA β αB） to be a Hom-bialgebra （called the double biproduct Hom-bialgebra and denoted by （A H B, αA β αB）） are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra （A H B, αA β） to be quasitriangular are given.
