In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras.A duality theorem for L-R crossed coproduct is proved.
In this paper, the notion of a twisted partial Hopf coaction is introduced. The conditions on partial cocycles are established in order to construct partial crossed coproducts. Then the classification of partial crossed coproducts is discussed. Finally, some necessary and sufficient conditions for a class of partial crossed coproducts to be quasitriangular bialgebras are given.
