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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
