On formal series and infinite products over Lie algebras

D. P. Zhelobenko

Independent University of Moscow

Аннотация: 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.

Ключевые слова: Lie algebras, Kac–Moody algebras, enveloping algebras, quantum algebras, modules.

Представлено: Б. Н. Шапуков
Поступило: 27.07.1999

Язык публикации: английский

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