Geodesic
On the Cohomology of Split Lie Algebra Extensions
Journal of Lie theory, Tome 22 (2012) no. 1, pp. 1-15.

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

We introduce the notion of compatible actions in the context of split extensions of Lie algebras over a field k. Using compatible actions, we construct new resolutions to compute the cohomology of semi-direct products of Lie algebras and give an alternative way to construct the Hochschild-Serre spectral sequence associated to a split extension. Finally, we describe several instances in which this spectral sequence collapses at the second page and obtain a sharper bound for its length in the finite dimensional case.
Classification : 17B56, 18G60, 18G40
Mots-clés : Lie algebra cohomology, free resolutions, Hochschild-Serre spectral sequence 
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D. Degrijse; N. Petrosyan . On the Cohomology of Split Lie Algebra Extensions. Journal of Lie theory, Tome 22 (2012) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/JLT_2012_22_1_JLT_2012_22_1_a0/