Lie algebras with maximality condition for Abelian subalgebras. (Q1425512)

The authors study special Lie algebras over an arbitrary field. It is shown that the maximality condition for the Abelian subalgebras yields finite dimensionality for any generally special algebra. As a corollary an equivalence of two conditions of finite dimensionality of the algebra and Noetherianness of its universal enveloping algebra is established for the given class of Lie algebras.