The projective variety of Lie algebra structures on a 4-dimensional 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 answer a 1987 question by Kirillov and Neretin.
翻译:四维矢量空间的立象代数结构有四个不可减损的维度11。 我们用24个变量在多元环中计算出它们的主要理想。 通过列出它们的学位和Hilbert多边代数,我们更正了早期的出版物,并回答了Kirillov和Neretin1987年提出的一个问题。