Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

Details Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

2000-09-07

arxiv.org/abs/math/0009076v1

J. Pure Appl. Algebra 170 (2002) 29-34.

Mathematics

Rings and Algebras

6 pages, Latex2e

Scientific paper

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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