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math.RA2002
Automorphisms of quantum and classical Poisson algebras
Janusz Grabowski, Norbert Poncin
We prove Pursell-Shanks type results for the Lie algebra D(M) of all linear differential operators of a smooth manifold M, for its Lie subalgebra D^1(M) of all linear first-order d…
math.RA2000
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…