Then in [2], [3], [4] and [5], the authors have discussed the structures of twisted Hopf algebras and bitwisted Hopf algebras and studied some properties of their antipodes, and so on.

• 在文献[2]、[3]、[4]和[5]中；作者分别研究了扭Hopf代数和双扭Hopf代数的结构和反极元的性质等.；本文主要研究双扭Hopf代数的对偶空间；以及两个双扭Hopf代数的对偶关系