  In this paper, we mainly give the relation of Rota-Baxter operators on
cocommutative Hopf algebras and Hopf braces. By Hopf braces, we establish the
relation of relative Rota-Baxter operators on cocommutative Hopf algebras and
bijective 1-cocycle. Moreover, we give the notion of symmetric Hopf braces, and
establish the relation of symmetric Hopf braces and Rota-Baxter Hopf algebras.

Quantum Algebra;Rings and Algebras