Journal of Lie Theory

no. 2
On a Filtration of the Second Cohomology of Nilpotent Lie Algebras
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 551-573
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.
DOI: 10.5802/jolt.737
Classification: 17B56, 17B30
Keywords: Nilpotent Lie algebras, free Nilpotent Lie algebras, filtration second cohomology, second Betti number 
@article{JOLT_2013_23_2_a9,
     author = {D. Degrijse},
     title = {On a {Filtration} of the {Second} {Cohomology} of {Nilpotent} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {551--573},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.737},
     zbl = {1286.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.737/}
}
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D. Degrijse. On a Filtration of the Second Cohomology of Nilpotent Lie Algebras. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 551-573. doi: 10.5802/jolt.737

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