An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras
LinearAlgebraAppl_345_85.pdf 1.68 MB
Variety of Lie algebras
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.
Linear Algebra and its Applications
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Copyright (c) 2002 Elsevier Science Inc.
Graduate School of Integrated Arts and Sciences