论文标题
矢量捆绑包的同质操作员的谎言代数
Lie algebra of homogeneous operators of a vector bundle
论文作者
论文摘要
We prove that for a vector bundle $ E \to M$, the Lie algebra $\mathcal{D}_{\mathcal{E}}(E)$ generated by all differential operators on $E$ which are eigenvectors of $L_{\mathcal{E}},$ the Lie derivative in the direction of the Euler vector field of $E,$ and lie代数$ \ MATHCAL {d} _g（e）$由grothendieck构造在$ \ mathbb {r} - $ algebra $ \ mathcal {a}（e）（e）：= {\ rm pol}（e）$ fiber-fiberwise polynomial函数上，conciencide an Conconcienciens。 这使我们能够计算$ \ mathbb {r} - $ algebra $ \ mathcal {a}（e）$的所有派生，并获得$ \ Mathcal {a}（e）（e）（e）的零重量导数的Lie Algebra的明确描述。
We prove that for a vector bundle $ E \to M$, the Lie algebra $\mathcal{D}_{\mathcal{E}}(E)$ generated by all differential operators on $E$ which are eigenvectors of $L_{\mathcal{E}},$ the Lie derivative in the direction of the Euler vector field of $E,$ and the Lie algebra $\mathcal{D}_G(E)$ obtained by Grothendieck construction over the $\mathbb{R}-$algebra $\mathcal{A}(E):= {\rm Pol}(E)$ of fiberwise polynomial functions, coincide up an isomorphism. This allows us to compute all the derivations of the $\mathbb{R}-$algebra $\mathcal{A}(E)$ and to obtain an explicit description of the Lie algebra of zero-weight derivations of $\mathcal{A}(E).$
