Lie algebras with an algebraic adjoint representation revisited

A well-known theorem due to Zelmanov proves that a Lie PI-algebra with an algebraic adjoint representation over a field of characteristic zero is locally finite-dimensional. In particular, a Lie algebra (over a field of characteristic zero) whose adjoint representation is algebraic of bounded degree is locally finite-dimensional.

Using recent results on Jordan structures in Lie algebras, we prove in this paper a proposition from which Zelmanov's theorem for Lie PI-algebras with an algebraic adjoint representation over an algebraically closed field of characteristic zero, and its corollary for Lie algebras with an algebraic adjoint representation of bounded degree (over an arbitrary field of characteristic zero) are easily derived.

(This paper has appeared in manuscr. math 140 (2013), 363--376)

A. Fernández López < emalfer@uma.es >

Artem Yu. Golubkov < golubkov@mccme.ru >