## Calin Popescu

*Characteristic zero loop space homology for certain two-cones *

Comment.Math.Univ.Carolinae 40,3 (1999) 593-597. **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.

**Keywords:** two-cone, Moore loop space, differential graded Lie algebra, free Lie algebra on a graded module, universal enveloping algebra, Hopf algebra

**AMS Subject Classification:** 55P35, 55P62, 57T05, 17B70, 17B35

PDF