Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 23 (2013), No. 2, 551--573
Copyright Heldermann Verlag 2013

On a Filtration of the Second Cohomology of Nilpotent Lie Algebras

Dieter Degrijse
Etienne Sabbelaan 53, 8500 Kortrijk, Belgium

We study a known filtration of the second cohomology of a finite dimensional nilpotent Lie algebra g with coefficients in a finite dimensional nilpotent g-module M. This filtration is based upon a refinement of the correspondence between H2(g,M) and equivalence classes of abelian extensions of g by M. We give a different characterization of this filtration and as a corollary, we obtain an expression for the second Betti number of g. Using this expression, we find bounds for the second Betti number and derive a cohomological criterium for the existence of certain central extensions of g.

Keywords: Nilpotent Lie algebras, free Nilpotent Lie algebras, filtration second cohomology, second Betti number.

MSC: 17B56, 17B30

[ Fulltext-pdf  (390  KB)] for subscribers only.