论文标题
在Gel'Fand-Kolmogoroff类型上
On Gel'fand-Kolmogoroff type results
论文作者
论文摘要
我们证明，向量捆绑包$ e \ to m $的特征是所有差分运算符在$ e $上生成的lie代数的符号的关联结构，这是lie派生词的特征向量，沿欧拉矢量字段的方向。 我们还通过$ \ mathbb {r} - 平滑功能的$代数获得类似的结果，这些功能是$ E的多项式。
We prove that a vector bundle $ E \to M$ is characterized by the associative structure of the space of symbols of the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. We also obtain similar result with the $\mathbb{R}-$ algebra of smooth functions which are polynomial along the fibers of $E.$ This allows us to deduce a Gel'fand-Kolmogoroff type result for the $\mathbb{R}-$algebra ${\rm Pol}(T^*(M))$ of symbols of the differential operators of $M.$
