Quasidimodule Algebra And Yetter-drinfeld'd Quasimodule Algebra Over Hopf Quasigroups

In this paper,we give the relation between the Long skew Hopf quasigroup and the quasidimodule algebra,and study the relation between the Long skew copaired Hopf coquasigroup and the quasidimodule coalgebra,and build the relation between the braided Hopf quasigroup and Yetter-Drinfel'd quasimodule algebra.In chapter 2,we give a sufficient and necessary condition for a Long skew Hopf quasigroup to be a right H-quasidimodule algebra.In chapter 3,we give a sufficient and necessary condition for a Long skew copaired Hopf coquasigroup to be a right H-quasidimodule coalgebra.In chapter 4,we study the relation between the braided Hopf quasigroup and the Yetter-Drinfel'd quasimodule algebra,and give a sufficient and necessary condition for a braided product to be a Long-Hopf quasigroup.In chapter 5,we construct the quantization of Long skew Hopf quasigroup by Harrison 2-cocycle,and also study the dual situation.