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 $FH(\Omega X; R)$ 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 $\Omega$ for the Moore loop space functor.
@article{119114,
author = {Calin Popescu},
title = {Characteristic zero loop space homology for certain two-cones},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {593-597},
zbl = {1009.55005},
mrnumber = {1732477},
language = {en},
url = {http://dml.mathdoc.fr/item/119114}
}
Popescu, Calin. Characteristic zero loop space homology for certain two-cones. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 593-597. http://gdmltest.u-ga.fr/item/119114/
Homotopy exponents for spaces of category two, Algebraic Topology, Proceedings, Arcata, 1986, Lecture Notes in Math., vol. 1370, pp.24-52, Springer-Verlag, Berlin, New York, 1989. | MR 1000365 | Zbl 0671.55009
Hopf algebras up to homotopy, J. Amer. Math. Soc. 2 (1989), 417-453. (1989) | MR 0991015 | Zbl 0681.55006
Torsion in homotopy groups, Ann. of Math. 109 (1979), 121-168. (1979) | MR 0519355
Universal enveloping algebras and loop space homology, J. Pure Appl. Algebra 83 (1992), 237-282. (1992) | MR 1194839 | Zbl 0769.57025
On the structure of Hopf algebras, Ann. of Math. 81 (1965), 211-264. (1965) | MR 0174052 | Zbl 0163.28202
On the homology of free Lie algebras, Comment. Math. Univ. Carolinae 39 (1998), 661-669. (1998) | MR 1715456 | Zbl 1059.17503