Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

Mark J. Gotay, Janusz Grabowski, Bryon Kaneshige

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 c…