On cohomology of split Lie algebra extensions

Details On cohomology of split Lie algebra extensions On cohomology of split Lie algebra extensions

2009-11-03

arxiv.org/abs/0911.0545v2

Journal of Lie Theory, 22 (1) (2012), 1-15

Mathematics

Algebraic Topology

21 pages

Scientific paper

We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of Lie algebras. We also give an alternative way to construct the Hochschild-Serre spectral sequence associated to a split extension of finite dimensional Lie algebras and obtain a sharper bound for the length of this spectral sequence.

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