Research On Several Questions In Weak Hopf Algebras

The aim of this dissertation is to further study weak Hopf algebra from five aspects as follows.In Part One,we discuss the theory of the actions of weak Hopf algebras on algebras,and not only prove that there exists a subalgegra of A#H which is isomorphic to A~H ,but also reveal that the constructure of A#H influence the relations between A and A#H.In Part Two,we discuss the conditions for biproduct to be an weak Hopf algebra,and give a sufficient condition for biproduct to be a weak Hopf algebra.In Part Three,we study the trace function of End_k(H) in weak algebras,and characterize the expression in terms of non-degenerated integrals.In Part four,Let H be a weak Hopf algebras over a field k and B an A-comodule algebra.we consider one Maschke question:first,for an exact sequence of (H, B)-Hopf modules which splits B linearly,when does it split (H, B) lin-early?...