Journal of Lie Theory

no. 1
On the Cohomology of Split Lie Algebra Extensions
Dieter Degrijse1; Nansen Petrosyan1
1Dept. of Mathematics, K.U. Leuven-Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium
Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 1-15
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.
DOI: 10.5802/jolt.659
Classification: 17B56, 18G60, 18G40
Keywords: Lie algebra cohomology, free resolutions, Hochschild-Serre spectral sequence

Dieter Degrijse  1 ; Nansen Petrosyan  1

1 Dept. of Mathematics, K.U. Leuven-Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium 
Dieter Degrijse; Nansen Petrosyan. On the Cohomology of Split Lie Algebra Extensions. Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 1-15. doi: 10.5802/jolt.659
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