# Polynomial Identities of Finite Dimensional Lie Algebras

## Author

**Alexandre V. Iltyakov**

## Status

Research Report 98-6

Date: 9 March 1998

## Abstract

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

## Content

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