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 e-prints
- Pub Date:
- September 2000
- DOI:
- 10.48550/arXiv.math/0009076
- arXiv:
- arXiv:math/0009076
- Bibcode:
- 2000math......9076G
- Keywords:
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- Mathematics - Rings and Algebras;
- Mathematics - Symplectic Geometry
- E-Print:
- 6 pages, Latex2e