Finite basis property of varieties of Lie algebras over a field of characteristic zero
A variety of algebras is called Spechtian if any of its subvarieties has a finite basis of identities. \textit{I. B. Volichenko} [Sib. Mat. Zh. 25, No.3, 40-54 (1984; Zbl 0575.17006)] proved that the variety \({\mathfrak AN}_ 2\) is Spechtian, where \({\mathfrak A}\) is the variety of all abelian Lie algebras, \({\mathfrak N_ n}\) is the variety of all nilpotent of degree n Lie algebras over a field of characteristic zero. Let \({\mathfrak E}\) denote the trivial variety, then the author proves that for any n the variety \({\mathfrak G}^{(n)}={\mathfrak AN}_ n\cup [{\mathfrak A}^ 2,{\mathfrak E}]\) has a finite basis of identities and the variety \({\mathfrak G}^{(2)}\) is Spechtian. The last result generalizes the above mentioned theorem of I. B. Volichenko.
scientific article; zbMATH DE number 4160968