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
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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 
@article{JLT_2008_18_2_JLT_2008_18_2_a9,
     author = {M. Stroppel},
     title = {The {Klein} {Quadric} and the {Classification} of {Nilpotent} {Lie} {Algebras} of {Class} {Two}},
     journal = {Journal of Lie theory},
     pages = {391--411},
     year = {2008},
     volume = {18},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_2_JLT_2008_18_2_a9/}
}
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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/