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- W3046100909 abstract "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 $mathcal{A}(E).$" @default.
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- W3046100909 date "2020-07-29" @default.
- W3046100909 modified "2023-09-27" @default.
- W3046100909 title "Lie algebra of homogeneous operators of a vector bundle" @default.
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