Geometry of central extensions of nilpotent Lie algebras

Abstract

We obtain a recurrent and monotone method for constructing and classifying nilpotent Lie algebras by means of successive central extensions. It consists in calculating the second cohomology of an extendable nilpotent Lie algebra with the subsequent study of the orbit space geometry of the automorphism group action on Grassmannians defined in terms of the second cohomology of the extendable nilpotent Lie algebra. Such a geometric method allows to classify some classes of nilpotent Lie algebras. The concept of a rigid central extension is introduced.