Abstract
Let H be a bialgebra. Let be a linear map, where A is a left H-comodule coalgebra, and an algebra with a left H-weak action Let be a linear map, where B is a right H-comodule coalgebra, and an algebra with a right H-weak action In this paper, we improve the necessary conditions for the two-sided crossed product algebra and the two-sided smash coproduct coalgebra to form a bialgebra (called double crossed biproduct) such that the condition in Majid’s double biproduct (or double-bosonization) is one of the necessary conditions. On the other hand, we provide a more general two-sided crossed product algebra structure via Brzezński’s crossed product and give some applications.
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