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KOSTANT'S THEOREM FOR SPECIAL FILTERED ALGEBRAS

Published online by Cambridge University Press:  10 March 2005

VYACHESLAV FUTORNY  and
SERGE OVSIENKO
VYACHESLAV FUTORNY
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, CEP 05315–970, Brazilfutorny@ime.usp.br
SERGE OVSIENKO
Affiliation:
Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Vladimirskaya 64, 01033, Kiev, Ukraineovsienko@zeos.net
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Abstract

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.

Keywords

13A0216W7017B3781R10
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 187 - 199
Copyright
© The London Mathematical Society 2005

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