Automorphisms and derivations of abelian extensions of some Lie algebras
type: Item
instance of: scholarly article
title: Automorphisms and derivations of abelian extensions of some Lie algebras
zbMATH Open document ID: 0780.17020
DOI: 10.1007/BF02941617
author: Yuri Bahturin
author: S. Zh. Nabiev
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1993-08-31T00:00:00Z
review text: Let \(L\) be a free Lie algebra, \(R\) an ideal of \(L\). An automorphism \(L/R\) is called tame if it is induced by an automorphism of \(L\) leaving \(R\) invariant. The authors prove that if \(K\) is an integral domain and \(M_ n= L/(L^ 2)^ 2\) a free metabelian algebra over \(K\) of rank \(n\), then any inner automorphism \(e^{\text{ad z}}\), \(z\in M^ 2\), is not tame. They consider similar problems for abelian extensions and derivation algebras and in particular, they prove that the derivation algebra \(\text{Der} M_ n\) of the free metabelian algebra of rank \(n>1\) is not finitely generated.
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 404307
zbMATH Keywords: automorphism
zbMATH Keywords: free metabelian algebra
zbMATH Keywords: abelian extensions
zbMATH Keywords: derivation algebras
reviewed by: Melih Boral
MaRDI profile type: Publication
cites work: Q3996716
cites work: Subalgebras of Free Associative Algebras
cites work: Q3348132
cites work: Automorphisms of Free Nilpotent Lie Algebras
cites work: Q4774166
description: scientific article; zbMATH DE number 404307