The occurrence problem for Lie algebras
type: Item
instance of: scholarly article
title: The occurrence problem for Lie algebras
zbMATH Open document ID: 0821.17002
DOI: 10.1007/BF02261696
published in: Algebra and Logic
publication date: 1995-04-20T00:00:00Z
review text: The author proves undecidability of the occurrence problem for: 1) finitely generated right ideals in the universal enveloping algebra of a free metabelian Lie algebra of a large enough rank (Theorem 1); 2) finitely generated subalgebras of a free solvable Lie algebra of solvability index \(\geq 3\) and of a large enough rank (Theorem 2); 3) finitely generated subalgebras of the free product \(L*L_ 1\) where \(L\) is a free metabelian Lie algebra of a large enough rank and \(L_ 1\) is a one-dimensional Lie algebra (Theorem 3). Theorem 3 gives the negative answer to G. Kukin's problem 1.86 in [Dnestr. Notebook, Novosibirsk (1982; Zbl 0493.16001)].
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 738952
zbMATH Keywords: free algebra
zbMATH Keywords: undecidability
zbMATH Keywords: occurrence problem
zbMATH Keywords: universal enveloping algebra
zbMATH Keywords: free metabelian Lie algebra
zbMATH Keywords: free solvable Lie algebra
author: Ualbai Umirbaev
reviewed by: Boris Vernikov
MaRDI profile type: Publication
Wikidata QID: Q115392641
cites work: Q5821489
cites work: Q4297725
cites work: Finite separability of groups and Lie algebras
cites work: A solvable group admitting a regular splitting automorphism of prime order is nilpotent
cites work: Q3289052
full work available at URL: https://doi.org/10.1007/bf02261696
OpenAlex ID: W2046723658
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description: scientific article; zbMATH DE number 738952