Journal of Lie Theory 18 (2008), No. 2, 391--411
Copyright Heldermann Verlag 2008
The Klein Quadric and the Classification of Nilpotent Lie Algebras of Class Two
Markus Stroppel
Institut für Geometrie und Topologie, Universität Stuttgart, 70550 Stuttgart, Germany
stroppel@igt.uni-stuttgart.de
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.
Keywords: Klein quadric, Grassmann space, orbit, nilpotent Lie algebra, Heisenberg algebra, classification.
MSC: 17B30, 22E25, 15A63, 15A69, 15A72, 51A50, 51E24
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