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 as Hopf braces, where 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.