On Hopf algebra structures over free operads
arXiv:math/0504531
Abstract
The operad Lie can be constructed as the operad of primitives Prim As from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincare'-Birkhoff-Witt and Cartier-Milnor-Moore. We replace As by families of free operads P, which include the operad Mag freely generated by a noncommutative non-associative binary operation and the operad of Stasheff polytopes. We obtain Poincare'-Birkhoff-Witt type theorems and collect information about the operads Prim P, e.g. in terms of characteristic functions.
25pages, uses elsart.cls, paper extracted from habilitation thesis (math.RA/0407074), revised (more details in sections 2,3,4, and 6)