一类Hopf代数的分解

The Factorization of a Class Hopf Algebras

(A,SA)和(H,SH)都是数域k上的Hopf代数,并且A是右H-余模代数.证明了:若存在H到A的代数同态i,i同时还是H-余模同态使得i SH=SA i,则存在A的一个子代数B,可在k空间B H上定义代数和余代数结构、对极使其成为与A同构的Hopf代数.

In this paper, （A,SA） and （H,SH） both are Hopf algebras on a field k . A is also an H-module algebra. We prove：If there is an algebra and H-comodule map i： H→A such that i . SH=SA . i ,we can get a subalgebra B of A. Then we define an algebra structure, a coalgebra structure and an antipode on the k-space such that it becomes an Hopf algebra which is isomorphic with A as Hopf algebras.