On a refinement of Ado's theorem
type: Item
instance of: scholarly article
title: On a refinement of Ado's theorem
zbMATH Open document ID: 0904.17006
author: Dietrich Burde
published in: Archiv der Mathematik
publication date: 1999-01-18T00:00:00Z
review text: The author studies the minimal dimension \(\mu(g)\) of a faithful \(g\)-module for \(n\)-dimensional nilpotent Lie algebras \(g\) (the nilpotent case is of particular interest since the invariant can be difficult to compute in this case). A known upper bound for \(\mu(g)\) of \(n^n+1\) is significantly improved to \(\alpha 2^n/\sqrt n\), where \(\alpha\sim 2.76287\), and much sharper upper bounds are obtained for various special classes of nilpotent Lie algebras such as filiform algebras and those admitting affine structures.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1145391
zbMATH Keywords: minimal dimension
zbMATH Keywords: Ado's theorem
zbMATH Keywords: nilpotent Lie algebra
zbMATH Keywords: faithful module
zbMATH Keywords: filiform algebras
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
full work available at URL: s000130050173
OpenAlex ID: W1994266008
DOI: 10.1007/S000130050173
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description: scientific article; zbMATH DE number 1145391