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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.
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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