Cohomology ring of a Lie algebra

asked 2020-08-21 07:41:36 -0500

Gabriel Pallier gravatar image

I would like to compute the cup products in cohomology for certain families of nilpotent Lie algebras over R. So far I could access to the cochain complex and compute the Betti numbers using the method chevalley_eilenberg_complex(). On the other hand, I see that the cup product of the cohomology ring of a cell complex can be computed.

So, is there a way to compute the cup products starting from the Lie algebra?

(Note that the Lie algebras that I consider are not always defined over the rational field, so that the cohomologies that I am interested in is not always that of a space of which I could describe the homotopy type by giving a cell complex.)

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