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zbMATH Open
Article . 1999
Data sources: zbMATH Open
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Journal of Lie Theory
Article . 1999
Data sources: u:cris
Journal of Lie Theory
Article . 1999 . Peer-reviewed
Data sources: Crossref
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Degenerations of Nilpotent Lie Algebras

Degenerations of nilpotent Lie algebras
Authors: Burde, Dietrich;

Degenerations of Nilpotent Lie Algebras

Abstract

Summary: In this paper we study degenerations of nilpotent Lie algebras. If \(\lambda,\mu\) are two points in the variety of nilpotent Lie algebras, then \(\lambda\) is said to degenerate to \(\mu\), \(\lambda \rightarrow_{\text{deg}} \mu\), if \(\mu\) lies in the Zariski closure of the orbit of \(\lambda\). It is known that all degenerations of nilpotent Lie algebras of dimension \(n <7\) can be realized via a one-parameter subgroup. We construct degenerations between characteristically nilpotent filiform Lie algebras. As an application it follows that for any dimension \(n \geq 7\) there exist examples of degenerations of nilpotent Lie algebras which cannot be realized via a one-parameter subgroup.

Country
Austria
Related Organizations
Keywords

Solvable, nilpotent (super)algebras

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
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