Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be...Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.展开更多
For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum ...For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.展开更多
We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of...We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of a conjecture of Yau(1998).They will also be useful in the problem of decomposition of tensor products of modules.Additionally,we give another generalization of result of Xi(2012)in terms of Chevalley-Eilenberg complex.展开更多
基金Supported by the National Natural Science Foundation of China(60873267)the Ningbo Natural Science Foundation of China(2011A610172)K.C.Wang Magna Fund in Ningbo University
文摘Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.
基金Supported by Doctoral Foundation of Qingdao University of Science and Technology (20080022398)the National Natural Science Foundation of China (11271318, 11171296)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110101110010)
文摘For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.
基金supported by National Natural Science Foundation of China (Grant No. 11501546)
文摘We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of a conjecture of Yau(1998).They will also be useful in the problem of decomposition of tensor products of modules.Additionally,we give another generalization of result of Xi(2012)in terms of Chevalley-Eilenberg complex.
