Journal of Lie Theory

no. 1
On the Cohomology of Split Lie Algebra Extensions
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 
@article{JOLT_2012_22_1_a0,
     author = {D. Degrijse and N. Petrosyan},
     title = {On the {Cohomology} of {Split} {Lie} {Algebra} {Extensions}},
     journal = {Journal of Lie Theory},
     pages = {1--15},
     year = {2012},
     volume = {22},
     number = {1},
     doi = {10.5802/jolt.659},
     zbl = {1302.17030},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.659/}
}
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D. Degrijse; N. 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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