The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in ...The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.展开更多
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.
The construction of the biproduct of Hopf algebras, which consists of smash product and the dual notion of smash coproduct, was first formulated by Radford. In this paper we study the quasitriangular structures over b...The construction of the biproduct of Hopf algebras, which consists of smash product and the dual notion of smash coproduct, was first formulated by Radford. In this paper we study the quasitriangular structures over biproduct Hopf algebras B*H. We show the necessary and sufficient conditions for biproduct Hopf algebras to be quasitriangular. For the case when they are, we determine completely the unique formula of the quasitriangular structures. And so we find a way to construct solutions of the Yang-Baxter equation over biproduct Hopf algebras in the sense of (Majid, 1990).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
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
In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we comput...In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.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
In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and su？cient conditions for the new object to be a Hopf group coalgebra.
基金The NSF (200510476001) of Education Department of Henan Province.
文摘The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.
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The construction of the biproduct of Hopf algebras, which consists of smash product and the dual notion of smash coproduct, was first formulated by Radford. In this paper we study the quasitriangular structures over biproduct Hopf algebras B*H. We show the necessary and sufficient conditions for biproduct Hopf algebras to be quasitriangular. For the case when they are, we determine completely the unique formula of the quasitriangular structures. And so we find a way to construct solutions of the Yang-Baxter equation over biproduct Hopf algebras in the sense of (Majid, 1990).
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.
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 Xunta de Galicia (Grant No. PGIDT07PXB322079PR)Ministerio de Educación (Grant Nos. MTM2007-62427, MTM2006-14908-CO2-01)FEDER
文摘In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.
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)
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 NSF of China(10771183、11201231)Docurate Foundation of Ministry of Education of China(200811170001)Jiangsu Planned Projects for Postdoctoral Research Funds(1102041C)~~
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 Fund of the Key Disciplines of Xinjiang Uygur Autonomous Region(2012ZDXK03)
文摘In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and su？cient conditions for the new object to be a Hopf group coalgebra.
