相对Hopf模和广义cleft扩张

RELATIVE HOPF MODULES AND GENERALIZED CLEFT EXTENSIONS

本文研究了π-cleft扩张的余代数分解问题及对偶的η-cocleft扩张的代数分解问题.利用相对Hopf模结构定理,给出了一个条件,使得具有余代数结构的π-cleft扩张有较好的余代数分解形式.作为特例,可以重新得到Radford给出的具有投射的双代数的双积分解定理.

In this article,the coalgebra factorization for a π-cleft extension and the algebra factorization for an η-cocleft extension are studied.Using the factorization theorem of relative Hopf modules,the authors give a condition for the π-cleft extension with a coalgebra structure to admit a nice coalgebra factorization.As a special case,the biproduct factorization for a bialgebra with a projection given by Radford can be re-obtained.