Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

Gotay, Mark J.; Grabowski, Janusz; Kaneshige, Bryon

Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

Authors

Gotay, Mark J.

Grabowski, Janusz

Kaneshige, Bryon

Description

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