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Algèbres de Poisson et algèbres de Lie résolubles

Patrice Tauvel·Rupert W. T Yu
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Abstract

Let $\mathfrak{g}$ be a solvable Lie algebra and $Q$ an $ad \mathfrak{g}$-stable prime ideal of the symmetric algebra $S(\mathfrak{g})$ of $\mathfrak{g}$. If $E$ is the set of non zero elements of $S(\mathfrak{g})/Q$ which are eigenvectors for the adjoint action of $\mathfrak{g}$ in $S(\mathfrak{g})/Q$, the localised algebra $(S(\mathfrak{g})/Q)_{E}$ has a natural structure of Poisson algebra. We study this algebra here.

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Patrice Tauvel, Rupert W. T Yu. 2007-02-21. Algèbres de Poisson et algèbres de Lie résolubles. https://arxiv.org/abs/math/0702615

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