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Characteristic zero loop space homology for certain two-cones. (English) Zbl 1009.55005
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.
##### MSC:
 55P35 Loop spaces 57T05 Hopf algebras (aspects of homology and homotopy of topological groups) 55P62 Rational homotopy theory 17B70 Graded Lie (super)algebras 17B35 Universal enveloping (super)algebras
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