An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras Original Research Article

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 logical and2V*circle times operatorV(V=C4) up to degree 3, 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.