Restricted Hom-type Extending Structures

The extending structure problem is a famous and still open problem.If we apply it to Hopf algebra,we can get the(H-C)extending structure problem.Agore and Militaru have solved the expending structure problem with the additional conditions,that is,the restricted(H-C)extending structure problem.The monoidal Hom-Hopf algebra is an important gen-eralization form of Hopf algebra,and it has developed into an important research direction,which injects vitality into the study of Hopf algebra.In this thesis,the extending structure problem is considered in the framework of monoidal Hom-Hopf algebra,it mainly focuses on the restricted Hom-type extending structure problem in the following aspects:(1)By introducing the monoidal Hom-bialgebra extending structure and the monoidal Hom-unified product,the sufficient and necessary conditions for monoidal Hom-unified prod-uct to be monoidal Hom-bialgebra are given,and then the antipode for monoidal Hom-unified product to be monoidal Hom-Hopf algebra is given.(2)By discussing the relationship between the different Hom-unified products corre-sponding to the different monoidal Hom-bialgebra extending structures,we establish the conditions for the isomorphism of the monoidal Hom-unified products,and solve the classi-fication in the restricted Hom-type extending structure problem.