Character Algebra And Application Of Integral In Weak Hopf Algebra

In this paper, we mainly study β-character algebras of weak Hopf algebras, homomorphisms, separable extensions of weak smash products on weak module algebras and weak structure theorem in the category of weak (H, A)—Hopf-module.In chapter one, we introduce the recent development of weak Hopf algebras, and study background, the main results and preliminaries in this paper.In chapter two, we concern with the β-character algebras in the case of weak Hopf algebras. We present a sufficient and necessary condition for the existence of the β-character algebras.In chapter three, we give a sufficient and necessary condition for the weak smash product A#H to be a separable extension on the weak module algebra, and present a sufficient and necessary condition for HomA#H(A,A#H) to be non-trivial, finally, we give the weak structure theorem in the category of weak (H,A)-Hopf module.