On the homology of free Lie algebras
Popescu, Calin
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 661-669 / Harvested from Czech Digital Mathematics Library
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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 $ \Bbb{L} {F\kern -0.8pt H}(V) \rightarrow {F\kern -0.8pt H} \Bbb{L} (V)$ is an isomorphism of graded Lie algebras over $R$, and deduce thereby that the natural arrow ${U\kern -1pt F\kern -0.8pt H}\Bbb{L} (V) \rightarrow {F\kern -0.8pt H\kern -0.4pt U} \Bbb{L} (V)$ is an isomorphism of graded cocommutative Hopf algebras over $R$; as usual, $F$ stands for free part, $H$ for homology, $\Bbb{L}$ for free Lie algebra, and $U$ for universal enveloping algebra. Related facts and examples are also considered.

Publié le : 1998-01-01
Classification:  17B01,  17B35,  17B55,  17B70 
@article{119042,
     author = {Calin Popescu},
     title = {On the homology of free Lie algebras},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {661-669},
     zbl = {1059.17503},
     mrnumber = {1715456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119042}
}

Popescu, Calin. On the homology of free Lie algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 661-669. http://gdmltest.u-ga.fr/item/119042/

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