Maschke Theorem And Fundamental Theorem Over Weak Hopf Algebras

This paper mainly gives the Maschke theorem for two-sided weak smash products, and the fundamental theorem of weak Hopf quantum Yang-Baxter modules over weak Hopf algebras, which generalize some results of [1, 8,12].The whole paper consists of four chapters.In chapter 1, we introduce the recent development of Hopf algebras (weak Hopf algebras), and the studied content and the main results in this paper.In chapter 2, we give the concept of two-sided smash products, and give a sufficient and necessary condition for two-sided smash products to be bialgebras (Hopf algebras), and give the Maschke theorem for two-sided smash products.In chapter 3, we introduce the concept of two-sided weak smash products, and we give some examples for two-sided weak smash products, and give the Maschke theorem for two-sided weak smash products.In chapter 4, we introduce the concept of weak Hopf quantum Yang-Baxter modules, and give the fundamental theorem of weak Hopf quantum Yang-Baxter modules.