Radford’s theorem about Hopf braces

Abstract

Let H be a Hopf algebra with bijective antipode. In this paper we prove that, if A is a Hopf brace with some projection on H, then there exists a compatible braided Hopf brace R such that A is isomorphic to $R♯H$ as Hopf braces, where $R♯H$ is some Radford’s biproduct Hopf algebra. This should be viewed as the brace version of well-known Radford’s theorem about Hopf algebras with a projection. This provides a new method to construct Hopf braces by some braided Hopf algebras.

Keywords:

• Hopf braces
• braided Hopf algebras
• Yang-Baxter equations
• Yetter-Drinfeld modules

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16T05
• 16K50

Acknowledgement

The authors would like to thank some referee for their constructive suggestions and valuable comments.

Additional information

Funding

This work was partially supported by the FNS of China (Grant No. 11302066) and NUPTSF (Grant No. NY220061).