D. P. Zhelobenko

On formal series and infinite products over algebras

(Lobachevskii Journal of Mathematics, Volume IV)

A brief survey of new methods for the study of nonstandard associative envelopes of Lie algebras is presented. Various extensions of the universal enveloping algebra U( g) are considered, where g is a symmetrizable Kac-Moody algebra. An elementary proof is given for describing the ``extremal projector'' over g as an infinite product over U ( g). Certain applications to the theory of g-modules are discussed.
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