Geodesic
On a Filtration of the Second Cohomology of Nilpotent Lie Algebras
Journal of Lie theory, Tome 23 (2013) no. 2, pp. 551-573.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B56, 17B30
Mots-clés : Nilpotent Lie algebras, free Nilpotent Lie algebras, filtration second cohomology, second Betti number 
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     author = {D. Degrijse },
     title = {On a {Filtration} of the {Second} {Cohomology} of {Nilpotent} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {551--573},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a9/}
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D. Degrijse . On a Filtration of the Second Cohomology of Nilpotent Lie Algebras. Journal of Lie theory, Tome 23 (2013) no. 2, pp. 551-573. http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a9/