  If $A$ is an associative algebra, then we can define the adjoint Lie algebra
$A^{(-)}$ and Jordan algebra $A^{(+)}$. It is easy to see that any associative
Rota--Baxter operator on $A$ induces a Lie and Jordan Rota--Baxter operator on
$A^{(-)}$ and $A^{(+)}$ respectively. Are there Lie (Jordan) Rota--Baxter
operators, which are not associative Rota--Baxter operators?
  In the present article we are studying these questions for the Sweedler
algebra $H_4$, that is a 4-dimension non-commutative Hopf algebra. More
precisely, we describe the Rota--Baxter operators on Lie algebra on the adjoint
Lie algebra $H_4^{(-)}$.
