Metabelian binary-Lie algebras (Q1058585)

A linear algebra A over a field F is called binary Lie if each two- generator subalgebra is a Lie algebra. We say that A is metabelian if \((A^ 2)^ 2=0\). Using an approach from a paper of \textit{Yu. A. Medvedev} [Algebra Logika 17, No.6, 705-728 (1978; Zbl 0425.16016)] the author shows that over an arbitrary field F of cardinality at least 4 and of characteristic different from 3 every metabelian variety of binary Lie algebras possesses a finite basis of identities. Another result, on residual finiteness of finitely generated metabelian binary Lie algebras, is easily translated from Lie algebra language [see the reviewer, Mat. Zametki 12, 713-716 (1972; Zbl 0249.17015)].