Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups
  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. 
Mark J. Gotay (University of Hawai`i), Janusz Grabowski (University of   Warsaw) and Bryon Kaneshige (University of Hawai`i)