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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:
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


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