Kostant theorem for special filtered algebras

V.Futorny, S.Ovsienko

Abstract

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

Keywords: Filtered algebra, complete intersection, Yangian, current algebra.

AMS Subject Classification: Primary 13A02; secondary 16W70, 17B37, 81R10.