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For a simple real Jordan algebra $V,$ a family of bi-differential operators from $\mathcal{C}^\infty(V\times V)$ to $\mathcal{C}^\infty(V)$ is constructed. These operators are covariant under the rational action of the conformal group of $V.$ They generalize the classical {\em Rankin-Cohen} brackets (case $V=\mathbb{R}$).

Conformally Covariant Bi-differential Operators on a Simple Real Jordan Algebra