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
Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduc...Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let （H, a） be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S（b×h）=（1B×SH（a^-1）b（-1）））（SB（b（0））×1H to be a monoidal Hom-Hopf algebra is derived.展开更多
Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic t...Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.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The National Natural Science Foundation of China(No.11371088,10871042,11571173)the Fundamental Research Funds for the Central Universities(No.KYLX15_0105)
文摘Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let （H, a） be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S（b×h）=（1B×SH（a^-1）b（-1）））（SB（b（0））×1H to be a monoidal Hom-Hopf algebra is derived.
基金Acknowledgements The authors sincerely thank the referees for their valuable suggestions and comments on this paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11601486, 61272007. 11401534）.
文摘Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.
