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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 arXiv:
 arXiv:math/0009076
 Bibcode:
 2000math......9076G
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Symplectic Geometry
 EPrint:
 6 pages, Latex2e