Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 8, No 1, (1986), 182p-191p
Metabelian varieties of Lie algebras over a finite field are studied in this paper. It is proved that any such variety is a union of two subvarieties. One of them is nilpotent and the other is generated by algebras which are abelian-by-abelian split extensions. Any proper subvariety of the metabelian variety is embedded in the variety generated by a wreath product of two finite dimensional abelian algebras. The proofs are based on the technique of varieties of representations of Lie algebras. Some other results concerning bivarieties of Lie algebras are obtained in the paper, too.