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ID 20313
file
creator
subject
Variety of Lie algebras
covariant
invariant
deformation
degeneration
abstract
We give an algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras from the representation theoretic viewpoint. For this purpose, we give the GL(V)-irreducible decomposition of the polynomial ring of the space ⋀2V* ⊗ V (V = C4) up to degree three, and show that intrinsic concepts defined by the vanishing of these covariants are sufficient to distinguish the isomorphism classes. As an application, we describe the variety of 4-dimensional Lie algebras and their degenerations in a comparatively simple form, by introducing a new family of normal forms of 4-dimensional Lie algebras that are just fitted for these purposes.
journal title
Linear Algebra and its Applications
volume
Volume 345
issue
Issue 1-3
start page
85
end page
118
date of issued
2002-04
publisher
Elsevier
issn
0024-3795
ncid
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
author
rights
Copyright (c) 2002 Elsevier Science Inc.
relation url
department
Graduate School of Integrated Arts and Sciences