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

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.

Presentation improved from the previous version, modified the examples. 16 pages

References in corpus (1)

• Six-dimensional nilpotent Lie algebras