论文标题
矢量束的古典泊松代数：谎言代数表征
Classical Poisson algebra of a vector bundle : Lie-algebraic characterization
论文作者
论文摘要
我们证明，线性操作员的符号的lie代数$ \ MATHCAL {s}（\ MATHCAL {p}（e，m））$，在矢量束$ e \ to m，$ $，$的表征。为了获得这一点，我们假设$ \ Mathcal {s}（\ Mathcal {p}（e，m））$被视为$ {\ rm c}^\ infty（m） - $模块，矢量捆绑包为$ n>1。一阶线性操作员的符号。我们获得了用$ \ MATHCAL {s}^1（\ MATHCAL {P}（E，M））$的向量捆绑包的谎言代数表征，而没有被视为$ {\ rm c}^\ infty（m） - $模块的假设。
We prove that the Lie algebra $\mathcal{S}(\mathcal{P}(E,M))$ of symbols of linear operators acting on smooth sections of a vector bundle $E\to M,$ characterizes it. To obtain this, we assume that $\mathcal{S}(\mathcal{P}(E,M))$ is seen as ${\rm C}^\infty(M)-$module and that the vector bundle is of rank $n>1.$ We improve this result for the Lie algebra $\mathcal{S}^1(\mathcal{P}(E,M))$ of symbols of first-order linear operators. We obtain a Lie algebraic characterization of vector bundles with $\mathcal{S}^1(\mathcal{P}(E,M))$ without the hypothesis of being seen as a ${\rm C}^\infty(M)-$module.
