关于切触射影向量场李超代数的矩阵实现$\mathfrak{spo}(2l+2|n)$
On the matrix realization of the Lie superalgebra of contact projective vector fields $\mathfrak{spo}(2l+2|n)$
摘要：
本文证明了李超代数$\mathfrak{spo}(2l+2|n)$是切触向量场李超代数$\mathcal{K}(2l+1|n)$与射影向量场李超代数$\mathfrak{pgl}(2l+2|n)$的交.我们主要使用P.Mathonet和F.“\textit{ Projectively equivariant quantizations over superspace $\mathbb{R}^{p|q}$. Lett. Math. Phys, 98: 311-331, 2011}“中的Radoux。说明了，我们使用嵌入的李超代数构成的矩阵属于$\gl(2l+2|n)$到$\mathrm{Vect}(\R^{2l+1|n})$。因此，我们在超维$2l+1-n$中推广，在$S^{1|2}$上的\cite{MelNibRad13}中描述的矩阵实现。我们提到，我们在这里证明的交集$\spo(2l+2|n)=\pgl(2l+2|n)\cap\cK(2l+1|n)$，在超级情况下，已经在\cite{CoOv12}的偶数情况下在$\R^{2l+2}$上得到了证明。
英文摘要：
In this paper, we show that the Lie superalgebra $\mathfrak{spo}(2l+2|n)$ is into 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 and F. Radoux in "\textit{ Projectively equivariant quantizations over superspace $\mathbb{R}^{p|q}$. Lett. Math. Phys, 98: 311-331, 2011}". Explicitly, we use the embedding of a Lie superalgebra constituted of matrices belonging to $\gl(2l+2|n)$ into $\mathrm{Vect}(\R^{2l+1|n})$. We generalize thus in superdimension $2l+1-n$, 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}.
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