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
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.
