Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

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

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

[ Fulltext-pdf  (274  KB)] for subscribers only.