Resumen de On Hopf algebra structures over free operads

Ralf Holtkamp

• The operad Lie can be constructed as the operad of primitives from the operad of associative algebras. This is reflected by the theorems of Friedrichs, Poincaré¿Birkhoff¿Witt and Cartier¿Milnor¿Moore. We replace the operad by families of free operads , which include the operad freely generated by a non-commutative non-associative binary operation and the operad of Stasheff polytopes. We obtain Poincaré¿Birkhoff¿Witt type theorems and collect information about the operads , e.g., in terms of characteristic functions.