An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras
Linear Algebra and its Applications Volume 345 Issue 1-3
Page 85-118
published_at 2002-04
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| File | |
| Title ( eng ) |
An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras
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| Creator | |
| Source Title |
Linear Algebra and its Applications
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| Volume | 345 |
| Issue | 1-3 |
| Start Page | 85 |
| End Page | 118 |
| 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.
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| Keywords |
Variety of Lie algebras
covariant
invariant
deformation
degeneration
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Elsevier
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| Date of Issued | 2002-04 |
| Rights |
Copyright (c) 2002 Elsevier Science Inc.
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0024-3795
[DOI] 10.1016/S0024-3795(01)00473-6
[NCID] AA00717292
[DOI] http://dx.doi.org/10.1016/S0024-3795(01)00473-6
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