# 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.