Geodesic
The Klein Quadric and the Classification of Nilpotent Lie Algebras of Class Two
Journal of Lie theory, Tome 18 (2008) no. 2, pp. 391-411.

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

We collect information about the Klein quadric which is useful to determine the orbits of the group of all linear bijections of a four-dimensional vector space on the Grassmann manifolds of the exterior product. This information is used to classify nilpotent Lie algebras of small dimension, over arbitrary fields (including the characteristic 2 case). The invariants used are easy to read off from any set of structure constants.
Classification : 17B30, 22E25, 15A63, 15A69, 15A72, 51A50, 51E24
Mots-clés : Klein quadric, Grassmann space, orbit, nilpotent Lie algebra, Heisenberg algebra, classification 
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     title = {The {Klein} {Quadric} and the {Classification} of {Nilpotent} {Lie} {Algebras} of {Class} {Two}},
     journal = {Journal of Lie theory},
     pages = {391--411},
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M. Stroppel . The Klein Quadric and the Classification of Nilpotent Lie Algebras of Class Two. Journal of Lie theory, Tome 18 (2008) no. 2, pp. 391-411. http://geodesic.mathdoc.fr/item/JLT_2008_18_2_JLT_2008_18_2_a9/