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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ideals of coadjoint orbits of nilpotent Lie algebras

Author: Colin Godfrey
Journal: Trans. Amer. Math. Soc. 233 (1977), 295-307
MSC: Primary 17B30
MathSciNet review: 0447359
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Abstract: For f a linear functional on a nilpotent Lie algebra g over a field of characteristic 0, let $J(f)$ be the ideal of all polynomials in $S(g)$ vanishing on the coadjoint orbit through f in ${g^\ast }$, and let $I(f)$ be the primitive ideal of Dixmier in the universal enveloping algebra $U(g)$, corresponding to the orbit. An inductive method is given for computing generators ${P_1}, \ldots ,{P_r}$ of $J(f)$ such that $\varphi {P_1}, \ldots ,\varphi {P_r}$ generate $I(f),\varphi$ being the symmetrization map from $S(g)$ to $U(g)$. Upper bounds are given for the number of variables in the polynomials ${P_i}$ and a counterexample is produced for upper bounds proposed by Kirillov.

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Keywords: Coadjoint orbits, nilpotent Lie algebra, primitive ideal, symmetrization map, universal enveloping algebra
Article copyright: © Copyright 1977 American Mathematical Society