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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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