The “Recognition Theorem” for graded Lie algebras is an essential
ingredient in the classification of finite-dimensional simple Lie algebras over
an algebraically closed field of characteristic p 3. The main goal of this
monograph is to present the first complete proof of this fundamental result.
Received by the editor September 16, 2005.
1991 Mathematics Subject Classification. Primary 17B50, 17B70, 17B20 Secondary
Key words and phrases. graded Lie algebras; simple Lie algebras of prime character-
istic; classical, Cartan type, and Melikyan Lie algebras.
∗The first author gratefully acknowledges support from National Science Foundation
grant #DMS–0245082 and from the E.B. Van Vleck Professorship at the University of
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