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On the structure of cofree Hopf algebras
-
Jean-Louis Loday
and
María Ronco
Published/Copyright:
May 4, 2006
Abstract
We prove an analogue of the Poincaré-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a nondifferential B∞-algebra. We construct a universal enveloping functor U2 from nondifferential B∞-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra ℋ is of the form U2(Prim ℋ). We take advantage of the description of the free 2as-algebra in terms of planar trees to unravel the operad associated to nondifferential B∞-algebras.
Received: 2005-03-18
Published Online: 2006-05-04
Published in Print: 2006-03-24
© Walter de Gruyter
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Articles in the same Issue
- Lines on projective hypersurfaces
- Almost isomorphism for countable state Markov shifts
- Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
- On the growth rate of the tunnel number of knots
- Signature homology
- On the structure of cofree Hopf algebras
- Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
- κ-types and Γ-asymptotic expansions
