扭曲双积Hopf代数的辫化结构

Braided structure on twisted biproduct Hopf algebra

设B和H都是Hopf代数,同时,B为左H-模余代数,左H-余模代数,H为右B-模余代数,则在B H上的交叉双积乘法和smash余积余乘相结合,可以构成一个Hopf代数,称为扭曲双积Hopf代数,记BH.自然会问BH何时成为辫化Hopf代数?当它是辫化Hopf代数时,其辫化结构又具何种形式?作者解答了这些问题,给出了扭曲双积Hopf代数成为辫化Hopf代数的一个充要条件.

Let B and H be two Hopf algebras, and let B be a left Hmodule coalgebra and a left Hcomodule algebra, H be a right Bmodule coalgebra such that the bicrossed product multiplication together with the smash coproduct comultiplication on B  H makes this a Hopf algebra, called a twisted biproduct Hopf algebra and denoted by BH. It is natural to ask when BH admits a braided structure, and what forms the braided structure of BH will take if BH admits a braided structure. An answer is given to these questions and the necessary and sufficient conditions are given for BH to be braided.