Hopf Algebra Structure On (m,k)-Hom-crossed(Co) Products

This thesis mainly studies the structure of Hom-crossed products,Hom-crossed coproducts and the cosemisimplicity of Hom-smash coproducts on the monoidal Hom-Hopf algebra.The whole paper consists of four chapters.In the first chapter,we introduce the history of Hopf algebra,the research background and main work of this thesis.In the second chapter,we introduce the(m,k)-Hom-crossed product,gives the necessary and sufficient conditions for it to be a monoidal Hom-bialgebra with the m-Hom-smash coproduct and derives a sufficient condition for this monoidal Hom-bialgebra to be a monoidal Hom-Hopf algebra.In the third chapter,we introduce the(n,l)-Hom-crossed coproduct,gives the necessary and sufficient conditions for it to be a monoidal Hom-bialgebra with the n-Hom-smash product and derives a sufficient condition for this monoidal Hom-bialgebra to be a monoidal Hom-Hopf algebra.In the fourth chapter,we study the cosemisimplicity of the Hom-smash coproduct and proves the Maschke theorem for it.