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
Dieter.Degrijse@kuleuven-kulak.be
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
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