论文标题
在刺刺类型的结果上
On Pursell-Shanks type results
论文作者
论文摘要
我们证明了对向量捆绑包的lie-elgebraic表征，用于lie代数$ \ MATHCAL {d}（e，m），$被视为$ {\ rm c}^\ infty（m） - $模块，所有线性运算符的全线性操作员，这些载体是根据vector bundle $ e \ e \ m $ $ $ $ $。 我们获得了所有线性一阶微分运算符的Lie subalgebra $ \ Mathcal {D}^1（e，m）$的结果。 多亏了精心挑选的过滤，$ \ nathcal {d}（e，m）$变为$ \ nathcal {p}（e，m）$，我们证明$ \ nathcal {p}^1（e，m）$表征了向量束，而没有被视为$ c}^\ infty的假设。 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） - $模块。 我们获得了类似的结果，该结果具有lie代数$ \ MATHCAL {s}^1（\ MATHCAL {p}（e，m））的一阶线性操作员的符号，而没有被视为$ {\ rm c}^\ infty（m） - $模块的假设。
We prove a Lie-algebraic characterization of vector bundle for the Lie algebra $\mathcal{D}(E,M),$ seen as ${\rm C}^\infty(M)-$module, of all linear operators acting on sections of a vector bundle $E\to M$. We obtain similar result for its Lie subalgebra $\mathcal{D}^1(E,M)$ of all linear first-order differential operators. Thanks to a well-chosen filtration, $\mathcal{D}(E,M)$ becomes $\mathcal{P}(E,M)$ and we prove that $\mathcal{P}^1(E,M)$ characterizes the vector bundle without the hypothesis of being seen as ${\rm C}^\infty(M)-$module. 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. We obtain a similar result with the Lie algebra $\mathcal{S}^1(\mathcal{P}(E,M))$ of symbols of first-order linear operators without the hypothesis of being seen as a ${\rm C}^\infty(M)-$module.
