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
通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D...通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D中的p维半单Hopf代数.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
We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was pre...We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.展开更多
基金Supported by China Postdoctoral Science Foundation(2017M611291)Foundation for Young Key Teacher by Henan Province(2015GGJS-088)Natural Science Foundation of Henan Province(17A110007)
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.
文摘通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D中的p维半单Hopf代数.
基金supported by China Postdoctoral Science Foundation(No.2017M611291)the Foundation for Young Key Teacher by Henan Province(No.2015GGJS-088)the Natural Science Foundation of Henan Province(No.17A110007)
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.
基金supported by projects MTM 2008-03339 from the Ministerio de Cienica e In,P07-FQM03128FQM0211 from Junta de Andalucía and TEC 2009-13763-C02-02
文摘We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.
