Partial (residual) Effects Of Hopf Group Algebra

Hopf π-coalgebra is an algebraic structure introduced by the famous topologist Tu-raev. As an extend of Hopf algebra, Hopf π-coalgebra draw wide research attention of mathematician and is studied deeply, After research, Many important conclusions of Hopf algebra also has been proved to be right on Hopf π-coalgebra.Partial action of group is defined by R. Exel and soonly become an effective tool in the research of C*-algebras generated by partial isometries on the Hilbert space. With the deepening of the research, partial group actions has become an independent and important branch of ring theory.Based on the above background. In this paper, we give a series of definations of partial Hopf π-coaction and partial Hopf π-comodule and so on.After that, we defined the partial π-tensor product, and proved that a partial π-tensor product of two partial Hopf π-comodule also is a partial Hopf π-comodule.Finally, we given the concept of partial π-smash product. Besides, we also given Morita, context.