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
In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit wit...A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit with a. noncocommutative Hopf superalgebra structure.展开更多
Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where th...Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where the opposite group S(π) of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.展开更多
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Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
文摘A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit with a. noncocommutative Hopf superalgebra structure.
基金The NSF (11101128) of Chinathe NSF (102300410049) of Henan Provincethe NSF (BK2012736) of Jiangsu Province
文摘Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where the opposite group S(π) of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.
基金Project supported by Guangxi Graduate Education Innovation Program(JGY2014092)Research Project and Youth Program of Guangdong University of Science&Technology(GKY-2016KYYB-15,GKY-2017KYQN-4)“Quality Project” of Guangdong University of Science and Technology in2016