Algorithmic problems for solvable Lie algebras
type: Item
instance of: scholarly article
title: Algorithmic problems for solvable Lie algebras
zbMATH Open document ID: 0445.17010
DOI: 10.1007/BF01674778
author: G. P. Kukin
published in: Algebra and Logic
publication date: 1979-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187021
review text: It is proved that any variety \(\mathfrak M\) of Lie algebras which contains the variety \(\mathfrak N_2\mathfrak A\), has the unsolvable word problem. This result is more general than the theorem of the reviewer about unsolvability of the word problem for the class of all Lie algebras [see Izv. Akad. Nauk SSSR, Ser. Mat. 36, 1173--1219 (1972; Zbl 0252.02046)] and gives the positive answer to the well-known problem of \textit{A. I. Shirshov} [see Dnestr Notebook, Novosibirsk, 1976, problem No. 155] about unsolvability of the word problem for the \(n\)-solvable Lie algebra, \(n\ge 3\).
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 03D40
zbMATH DE Number: 3695427
zbMATH Keywords: variety of Lie algebras
zbMATH Keywords: unsolvable word problem
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
Wikidata QID: Q115393246
cites work: Q4775864
cites work: The isomorphism problem for solvable groups
cites work: The subalgebras of free Lie \(p\)-algebras
cites work: Q5545593
description: scientific article; zbMATH DE number 3695427