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arXiv · 1204.4123

On a spectral sequence for the cohomology of a nilpotent Lie algebra

Viviana J. del Barco
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Abstract

Given a nilpotent Lie algebra $\mathfrak n$ we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the Lie algebra cohomology of $\mathfrak n$. The limit of this spectral sequence gives a grading for the Lie algebra cohomology, except for the cohomology groups of degree 0, 1, $\dim \mathfrak n-1$ and $\dim\mathfrak n$ as we shall prove. We describe the spectral sequence associated to a nilpotent Lie algebra which is a direct sum of two ideals, one of them of dimension one, in terms of the spectral sequence of the co-dimension one ideal. Also, we compute the spectral sequence corresponding to each real nilpotent Lie algebra of dimension less than or equal to six.

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Viviana J. del Barco. 2013-10-17. On a spectral sequence for the cohomology of a nilpotent Lie algebra. https://arxiv.org/abs/1204.4123

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