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Bulletin of the London Mathematical Society 2005 37(2):187-199; doi:10.1112/S0024609304003844
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© London Mathematical Society

Kostant's Theorem for Special Filtered Algebras

Vyacheslav Futorny and Serge Ovsienko

Instituto de Matemática e Estatística, Universidade de São Paulo Caixa Postal 66281, São Paulo, CEP 05315-970, Brazil futorny{at}ime.usp.br
Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University Vladimirskaya 64, 01033, Kiev, Ukraine ovsienko{at}zeos.net

Received 1 April 2003. Revision received 1 October 2003.

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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