| Title:
|
Characteristic zero loop space homology for certain two-cones (English) |
| Author:
|
Popescu, Calin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
593-597 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
two-cone |
| Keyword:
|
Moore loop space |
| Keyword:
|
differential graded Lie algebra |
| Keyword:
|
free Lie algebra on a graded module |
| Keyword:
|
universal enveloping algebra |
| Keyword:
|
Hopf algebra |
| MSC:
|
17B35 |
| MSC:
|
17B70 |
| MSC:
|
55P35 |
| MSC:
|
55P62 |
| MSC:
|
57T05 |
| idZBL:
|
Zbl 1009.55005 |
| idMR:
|
MR1732477 |
| . |
| Date available:
|
2009-01-08T18:55:39Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119114 |
| . |
| Reference:
|
[1] 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. Zbl 0671.55009, MR 1000365 |
| Reference:
|
[2] Anick D.J.: Hopf algebras up to homotopy.J. Amer. Math. Soc. 2 (1989), 417-453. Zbl 0681.55006, MR 0991015 |
| Reference:
|
[3] Cohen F.R., Moore J.C., Niesendorfer J.A.: Torsion in homotopy groups.Ann. of Math. 109 (1979), 121-168. MR 0519355 |
| Reference:
|
[4] Halperin S.: Universal enveloping algebras and loop space homology.J. Pure Appl. Algebra 83 (1992), 237-282. Zbl 0769.57025, MR 1194839 |
| Reference:
|
[5] Milnor J.W., Moore J.C.: On the structure of Hopf algebras.Ann. of Math. 81 (1965), 211-264. Zbl 0163.28202, MR 0174052 |
| Reference:
|
[6] Popescu C.: On the homology of free Lie algebras.Comment. Math. Univ. Carolinae 39 (1998), 661-669. Zbl 1059.17503, MR 1715456 |
| . |
