
Journal of Lie Theory 33 (2023), No. 3, 703712 Copyright Heldermann Verlag 2023 FourDimensional Lie Algebras Revisited Laurent Manivel Paul Sabatier University, Toulouse, France laurent.manivel@math.cnrs.fr Bernd Sturmfels (1) MaxPlanckInstitut MiS, Leipzig, Germany (2) Dept. of Mathematics, University of California, Berkeley, U.S.A. bernd@mis.mpg.de Svala Sverrisdóttir Dept. of Mathematics, University of California, Berkeley, U.S.A. svalasverris@berkeley.edu The projective variety of Lie algebra structures on a 4dimensional 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. Keywords: Classification of Lie algebras, irreducible component, degree, Hilbert polynomial, resolution of singularities. MSC: 14C17, 14M99, 17B05. [ Fulltextpdf (133 KB)] for subscribers only. 