Geodesic
The Variety of Lie Algebras of Maximal Class
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 184-201

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We present an explicit description of the affine variety $M_\mathrm{Fil}$ of Lie algebras of maximal class (filiform Lie algebras): the formulas of polynomial equations that determine this variety are written down. The affine variety $M_\mathrm{Fil}$ can be considered as the base of the nilpotent versal deformation of the $\mathbb N$-graded Lie algebra $\mathfrak m_0$. 
@article{TM_2009_266_a9,
     author = {D. V. Millionshchikov},
     title = {The {Variety} of {Lie} {Algebras} of {Maximal} {Class}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {184--201},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a9/}
}
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D. V. Millionshchikov. The Variety of Lie Algebras of Maximal Class. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 184-201. http://geodesic.mathdoc.fr/item/TM_2009_266_a9/