KOSTANT'S THEOREM FOR SPECIAL FILTERED ALGEBRAS

KOSTANT'S THEOREM FOR SPECIAL FILTERED ALGEBRAS

A famous result of Kostant's states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. An analogue of this result is proved for the class of special filtered algebras. This is then applied to show that the restricted Yangian and the unive...

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Veröffentlicht in:The Bulletin of the London Mathematical Society 2005-04, Vol.37 (2), p.187-199
Hauptverfasser: FUTORNY, VYACHESLAV, OVSIENKO, SERGE
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description A famous result of Kostant's states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. An analogue of this result is proved for the class of special filtered algebras. This is then applied to show that the restricted Yangian and the universal enveloping algebra of the restricted current algebra, associated with the general linear Lie algebra, are both free over their centers. 2000 Mathematics Subject Classification 13A02, 16W70, 17B37, 81R10.
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title KOSTANT'S THEOREM FOR SPECIAL FILTERED ALGEBRAS
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