Displaying similar documents to “On the homology of free Lie algebras”

Characteristic zero loop space homology for certain two-cones

Calin Popescu (1999)

Commentationes Mathematicae Universitatis Carolinae

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Given a principal ideal domain R of characteristic zero, containing 1/2, and a two-cone X of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra F H ( Ω X ; R ) to be isomorphic with the universal enveloping algebra of some R -free graded Lie algebra; as usual, F stands for free part, H for homology, and Ω for the Moore loop space functor.

The center of a graded connected Lie algebra is a nice ideal

Yves Félix (1996)

Annales de l'institut Fourier

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Let ( 𝕃 ( V ) , d ) be a free graded connected differential Lie algebra over the field of rational numbers. An ideal I in the Lie algebra H ( 𝕃 ( V ) , d ) is called if, for every cycle α 𝕃 ( V ) such that [ α ] belongs to I , the kernel of the map H ( 𝕃 ( V ) , d ) H ( 𝕃 ( V x ) , d ) , d ( x ) = α , is contained in I . We show that the center of H ( 𝕃 ( V ) , d ) is a nice ideal and we give in that case some informations on the structure of the Lie algebra H ( 𝕃 ( V x ) , d ) . We apply this computation for the determination of the rational homotopy Lie algebra L X = π * ( Ω X ) of a simply connected space X . We deduce...

Knit products of graded Lie algebras and groups

Michor, Peter W.

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Let A = k A k and B = k B k be graded Lie algebras whose grading is in 𝒵 or 𝒵 2 , but only one of them. Suppose that ( α , β ) is a derivatively knitted pair of representations for ( A , B ) , i.e. α and β satisfy equations which look “derivatively knitted"; then A B : = k , l ( A k B l ) , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra A ( α , β ) B . This graded Lie algebra is called the knit product of A and B . The author investigates the general situation for any graded Lie subalgebras A and...