Journal of Lie Theory

no. 3
Four-Dimensional Lie Algebras Revisited
Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 703-712
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.
DOI: 10.5802/jolt.1301
Classification: 14C17, 14M99, 17B05
Keywords: Classification of Lie algebras, irreducible component, degree, Hilbert polynomial, resolution of singularities 
@article{JOLT_2023_33_3_a0,
     author = {L. Manivel and B. Sturmfels and S. Sverrisd\~A3ttir},
     title = {Four-Dimensional {Lie} {Algebras} {Revisited}},
     journal = {Journal of Lie Theory},
     pages = {703--712},
     year = {2023},
     volume = {33},
     number = {3},
     doi = {10.5802/jolt.1301},
     zbl = {1522.14011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1301/}
}
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L. Manivel; B. Sturmfels; S. SverrisdÃ3ttir. Four-Dimensional Lie Algebras Revisited. Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 703-712. doi: 10.5802/jolt.1301

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