Fortieth Anniversary of Extremal Projector Method for Lie Symmetries

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A brief review of the extremal projector method for Lie symmetries (Lie algebras and superalgebras as well as their quantum analogs) is given. A history of its discovery and some simplest applications are presented.
14 pages, minor corrections, few references added. This version will be published in Contemporary Mathematics (Proc. of Conference on "Non-commutative Geometry in Mathematical Physics", Karshtad, July 2004)

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