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.