Characteristic zero loop space homology for certain two-cones
Commentationes Mathematicae Universitatis Carolinae (1999)
- Volume: 40, Issue: 3, page 593-597
- ISSN: 0010-2628
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topPopescu, Calin. "Characteristic zero loop space homology for certain two-cones." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 593-597. <http://eudml.org/doc/248444>.
@article{Popescu1999,
abstract = {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.},
author = {Popescu, Calin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {two-cone; Moore loop space; differential graded Lie algebra; free Lie algebra on a graded module; universal enveloping algebra; Hopf algebra; two-cone; Moore loop space; differential graded Lie algebra; free Lie algebra on a graded module; universal enveloping algebra; Hopf algebra},
language = {eng},
number = {3},
pages = {593-597},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characteristic zero loop space homology for certain two-cones},
url = {http://eudml.org/doc/248444},
volume = {40},
year = {1999},
}
TY - JOUR
AU - Popescu, Calin
TI - Characteristic zero loop space homology for certain two-cones
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 593
EP - 597
AB - 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.
LA - eng
KW - two-cone; Moore loop space; differential graded Lie algebra; free Lie algebra on a graded module; universal enveloping algebra; Hopf algebra; two-cone; Moore loop space; differential graded Lie algebra; free Lie algebra on a graded module; universal enveloping algebra; Hopf algebra
UR - http://eudml.org/doc/248444
ER -
References
top- Anick D.J., 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. Zbl0671.55009MR1000365
- Anick D.J., Hopf algebras up to homotopy, J. Amer. Math. Soc. 2 (1989), 417-453. (1989) Zbl0681.55006MR0991015
- Cohen F.R., Moore J.C., Niesendorfer J.A., Torsion in homotopy groups, Ann. of Math. 109 (1979), 121-168. (1979) MR0519355
- Halperin S., Universal enveloping algebras and loop space homology, J. Pure Appl. Algebra 83 (1992), 237-282. (1992) Zbl0769.57025MR1194839
- Milnor J.W., Moore J.C., On the structure of Hopf algebras, Ann. of Math. 81 (1965), 211-264. (1965) Zbl0163.28202MR0174052
- Popescu C., On the homology of free Lie algebras, Comment. Math. Univ. Carolinae 39 (1998), 661-669. (1998) Zbl1059.17503MR1715456
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