Four-Dimensional Lie Algebras Revisited

The projective variety of Lie algebra structures on a 4-dimensional complex vector space has four irreducible components of dimension 11. We compute their prime ideals in the polynomial ring in 24 variables. By listing their degrees and Hilbert polynomials, we correct an earlier publication and we solve a problem raised by Kirillov and Neretin in 1987. Mathematics Subject Classification: 14C17, 14M99, 17B05.