L-R Smash Product On BiHom-Hopf Algebras

In this thesis,we mainly study L-R smash product over BiHom-Hopf algebras,which are divided into three parts.Firstly,we introduce the notion of the BiHom-L-R smash product and give the necessary and sufficient conditions for the BiHom-L-R smash product and tensor coproduct to form a BiHom-bialgebra.Secondly,we study the Maschke-type theorem for the BiHom-L-R smash product over a finite dimension semisimple BiHom-Hopf algebra(H,αH,βH,ψH,ωH).Finally,we discuss a Morita con-text between BiHom-subalgebra(AbiH,αA |AbiH,βA|AbiH)and the BiHom-L-R smash product(A#H,αA(?)αH,βA(?)βH).