Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

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.

6 pages, Latex2e