Geodesic
Four-Dimensional Lie Algebras Revisited
Laurent Manivel1 ; Bernd Sturmfels2, 3 ; Svala Sverrisdóttir4
1Paul Sabatier University, Toulouse, France
2(1) Max-Planck-Institut MiS, Leipzig, Germany
3(2) Dept. of Mathematics, University of California, Berkeley, U.S.A.
4Dept. of Mathematics, University of California, Berkeley, U.S.A.
Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 703-712

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 14C17, 14M99, 17B05
Mots-clés : Classification of Lie algebras, irreducible component, degree, Hilbert polynomial, resolution of singularities

Laurent Manivel  1   ; Bernd Sturmfels  2 , 3   ; Svala Sverrisdóttir  4

1 Paul Sabatier University, Toulouse, France
2 (1) Max-Planck-Institut MiS, Leipzig, Germany
3 (2) Dept. of Mathematics, University of California, Berkeley, U.S.A.
4 Dept. of Mathematics, University of California, Berkeley, U.S.A. 
Laurent Manivel; Bernd Sturmfels; Svala Sverrisdóttir. Four-Dimensional Lie Algebras Revisited. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 703-712. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a0/
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