On formal series and infinite products over algebras
(Lobachevskii Journal of Mathematics, Vol.4, pp.207-218)

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 $U(\mathfrak g)$ are considered, where $\mathfrak g$ is a symmetrizable Kac-Moody algebra. An elementary proof is given for describing the ``extremal projector'' over $\mathfrak g$ as an infinite product over $U (\mathfrak g)$. Certain applications to the theory of $\mathfrak g$-modules are discussed.

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