Kostant theorem for special filtered algebras

Vyacheslav Futorny; Serge Ovsienko

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Kostant theorem for special filtered algebras

Vyacheslav Futorny·Serge Ovsienko

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Abstract

A famous result of Kostant states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. We prove an analogue of this result for a class of filtered algebras and apply it to show the freeness over its center of the restricted Yangian and the universal enveloping algebra of the restricted current algebra associated with the general linear Lie algebra.

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Vyacheslav Futorny, Serge Ovsienko. 2003-03-29. Kostant theorem for special filtered algebras. https://arxiv.org/abs/math/0303372

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