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Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

Mark J. Gotay·Janusz Grabowski·Bryon Kaneshige
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Abstract

We study the algebraic structure of the Poisson algebra P(O) of polynomials on a coadjoint orbit O of a semisimple Lie algebra. We prove that P(O) splits into a direct sum of its center and its derived ideal. We also show that P(O) is simple as a Poisson algebra iff O is semisimple.

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Mark J. Gotay, Janusz Grabowski, Bryon Kaneshige. 2000-09-07. Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups. https://arxiv.org/abs/math/0009076

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