Polynomial Identities of Finite Dimensional Lie Algebras


Alexandre V. Iltyakov


Research Report 98-6
Date: 9 March 1998


During a long time one of the central problem in the theory of associative algebras satisfying a polynomial identity (PI algebras) was Specht's conjecture saying that any associative algebra over a field of characteristic $0$ has a finite basis of polynomial identities. A positive solution was given by A.R.Kemer in 1987; His proof is based on a geometric approach due to Amitsur and accumulates ideas and results of many specialists on PI rings and algebras. Later, using the same approach, the author proved a similar statement in the class of finite dimensional Lie algebras. These notes gives the proof of that theorem in a revised form; they also includes Kemer's theorem adopted to the case of finitely generated algebras.

Key phrases

Associative and Lie algebras. polynomial identities.

AMS Subject Classification (1991)

Primary: 17B01
Secondary: 16R10


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