Abstract
By the Latyshev theorem, the universal enveloping algebra of a Lie algebra over a field of zero characteristic is a PI-algebra if and only if this Lie algebra is abelian. The Bakhturin theorem holds for each Lie algebra G of positive characteristic: The universal enveloping algebra has a nontrivial identity if and only if G is almost abelian and all inner derivations adx, x ~ G, are algebraic of bounded degree, depending only on G. This result was used by Bakhturin for the study of dimensions of irreducible representations of Lie algebras of positive characteristic. The proofs of these results are given in [i, Chap. 6] (see also [2-4]).
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