Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups

2000/09/07 by Mark J. Gotay, Janusz Grabowski, Bryon Kaneshige
Mathematics · #math.RA #math.SG

paper · pdf

published as J. Pure Appl. Algebra 170 (2002) 29-34. · 6 pages, Latex2e

arxiv created 2000/09/07 · arxiv updated 2009/11/30

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.

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