扭Smash双积

THE TWISTED SMASH BIPRODUCT

设H是双代数 ,A是H 双模代数 ,且为左H 余模余代数 .本文构造一种新的代数—扭Smash双积A×H ,推广了扭Smash积和Smash双积 .我们给出了扭Smash双积A×H作成双代数的充要条件 ,证明了当A ,H都是Hopf代数时 ,A×H 也是Hopf代数 ,利用映射系统刻画了双代数A×H的结构 ,并考虑了它的对偶情况 .

Let H be a bialgebra, and A an Hbimodule algebra and a left Hcomodule coalgebra. In this paper we construct a new algebra A×H, twisted Smash biproduct, and generalizes the twisted Smash product and the Smash biproduct. Suffcient and necessary conditions for A×H to be a bialgebra are given. In addition, we characterize the construction of A×H by using the mapping system and also consider its dual situation.