论文标题
关于载体束的泊松代数表征
On a Poisson-algebraic characterization of vector bundles
论文作者
论文摘要
我们证明，$ \ Mathbb {r} - $ algebra $ \ mathcal {s}（\ Mathcal {p}（e，m））的符号的符号的符号符号，这些符号是在vector $ e \ to m $ emopopted of sum \ [m $ e \ [sum \ [ \ Mathcal {s}（\ Mathcal {p}（e，m））= \ Mathcal {J}（e）\ oplus {\ rm pol}（t^*m）\]，其中$ \ nathcal {j}（j}（j}（e）$是$ \ nathcal of $ \ nathcal of tr t try of tr t tryt tt trt oftry of tr t try try oftry of tr t try oftry of。元素始终为零。这会导致$ \ MATHCAL {s}（\ Mathcal {p}（e，m））$无法将$ e \ to $ e \ to M $具有$ \ Mathbb {r} - $代数的唯一结构。我们证明，凭借其泊松代数结构，$ \ MATHCAL {s}（\ Mathcal {p}（e，m））$将矢量束$ e \ to M $表征为M $，而无需将要求视为$ {\ rm C}^\ infty（m） - $模块。
We prove that the $\mathbb{R}-$algebra $\mathcal{S}(\mathcal{P}(E,M)) $ of symbols of differential operators acting on the sections of the vector bundle $E\to M$ decompose into the sum \[ \mathcal{S}(\mathcal{P}(E,M))=\mathcal{J}(E)\oplus {\rm Pol}(T^*M) \] where $\mathcal{J}(E)$ is an ideal of $\mathcal{S}(\mathcal{P}(E,M))$ in which product of two elements is always zero. This induces that $\mathcal{S}(\mathcal{P}(E,M))$ cannot characterize $E \to M$ with its only structure of $\mathbb{R}-$ algebra. We prove that with its Poisson algebra structure, $\mathcal{S}(\mathcal{P}(E,M))$ characterizes the vector bundle $E\to M$ without the requirement to be considered as a ${\rm C}^\infty(M)-$module.
