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In this paper, we show that the Lie superalgebra $\mathfrak{spo}(2l+2|n)$ isinto the intersection of Lie superalgebra of contact vector fields$\mathcal{K}(2l+1|n)$ and the Lie superalgebra of projective vector fields$\mathfrak{pgl}(2l+2|n)$. We use mainly the embedding used by P. Mathonet andF. Radoux in "\textit{ Projectively equivariant quantizations over superspace$\mathbb{R}^{p|q}$. Lett. Math. Phys, 98: 311-331, 2011}". Explicitly, we usethe embedding of a Lie superalgebra constituted of matrices belonging to$\gl(2l+2|n)$ into $\mathrm{Vect}(\R^{2l+1|n})$. We generalize thus insuperdimension $2l+1-n$, the matrix realization described in \cite{MelNibRad13}on $S^{1|2}$. We mention that the intersection$\spo(2l+2|n)=\pgl(2l+2|n)\cap\cK(2l+1|n)$ that we prove here, in super case,has been prooved on $\R^{2l+2}$ in even case in \cite{CoOv12}.

On the matrix realization of the Lie superalgebra of contact projective vector fields $\mathfrak{spo}(2l+2|n)$