Finite basis property of varieties of Lie algebras over a field of characteristic zero
type: Item
instance of: scholarly article
title: Finite basis property of varieties of Lie algebras over a field of characteristic zero
zbMATH Open document ID: 0707.17002
author: L. V. Tsypunov
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 16R10
zbMATH DE Number: 4160968
zbMATH Keywords: Specht variety
zbMATH Keywords: finite basis of identities
reviewed by: Ivan Shestakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4160968