数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 613-620.
摘要: We develop the Radford’s biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B#×βαH and derive a necessary and sufficient condition for B#×βαH with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1].
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