Let H be a bialgebra. Let alpha : C -> H circle times H be a linear map, where C is a left H-module algebra, and a coalgebra with a left H-weak coaction. Let beta : D -> H circle times H be a linear map, where D is a right H-module algebra, and a coalgebra with a right H-weak coaction. In this paper, we extend the construction of two-sided smash coproduct to two-sided crossed coproduct C x(alpha) H-beta x D. Then we derive the necessary and sufficient conditions for two-sided smash product algebra C # H # D and C x(alpha) H-beta x D to be a bialgebra, which generalizes the Majid's double biproduct in Double-bosonization of braided groups and the construction of U-q(g), Math. Proc. Camb. Philos. Soc. 125(1) (1999) 151-192 and the Wang-Wang-Yao's crossed coproduct in Hopf algebra structure over crossed coproducts, Southeast Asian Bull. Math. 24(1) (2000) 105-113.
展开▼
