Corpus ID: 115178634

On cohomology of split Lie algebra extensions

  title={On cohomology of split Lie algebra extensions},
  author={Dieter Degrijse and Nansen Petrosyan},
  journal={arXiv: Algebraic Topology},
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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