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（C, α） and（H, β） be Hom-bialgebras and ω ： C H → H C a linear map.We introduce the concept of a Hom-ω-crossed coproduct（Cω σ H, γ） and we give necessary and sufficient conditions for the new object ...Let（C, α） and（H, β） be Hom-bialgebras and ω ： C H → H C a linear map.We introduce the concept of a Hom-ω-crossed coproduct（Cω σ H, γ） and we give necessary and sufficient conditions for the new object to be a Hom-Hopf algebra.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partially supported by the China Postdoctoral Science Foundation (No.2019M651764)National Natural Science Foundation of China (Grant No.11601231,No.11601233)the Natural Science Foundation of Jiangsu Province (Grant No.BK20160708)。
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.
文摘Let（C, α） and（H, β） be Hom-bialgebras and ω ： C H → H C a linear map.We introduce the concept of a Hom-ω-crossed coproduct（Cω σ H, γ） and we give necessary and sufficient conditions for the new object to be a Hom-Hopf algebra.
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.
