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On Leibniz homology

Teimuraz Pirashvili (1994)

Annales de l'institut Fourier

We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.

On the homology of free Lie algebras

Calin Popescu (1998)

Commentationes Mathematicae Universitatis Carolinae

Given a principal ideal domain R of characteristic zero, containing 1 / 2 , and a connected differential non-negatively graded free finite type R -module V , we prove that the natural arrow 𝕃 F H ( V ) F H 𝕃 ( V ) is an isomorphism of graded Lie algebras over R , and deduce thereby that the natural arrow U F H 𝕃 ( V ) F H U 𝕃 ( V ) is an isomorphism of graded cocommutative Hopf algebras over R ; as usual, F stands for free part, H for homology, 𝕃 for free Lie algebra, and U for universal enveloping algebra. Related facts and examples are also considered....

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