## Séminaire de Géométrie et Quantification |

**H.
Furusho, ****B.
Enriquez**

(Université de Nagoya, resp. Université de Strasbourg)

Lundi 25 septembre 15h30 puis 16h45, salle 221, IHP

*Titre:
**A
Betti counterpart of the harmonic coproduct *

Résumé :
In earlier work, we
proved that Racinet's double shuffle group is the
stabilizer of the harmonic coproduct defined on a subalgebra of the
free algebra over two generators relative to a certain action on this
algebra. This leads to the construction of a family of new coproducts
on the same algebra, depending on a scalar parameter, which are
related with one another by scaling transformations. The double
shuffle torsor can then be described as the set of elements taking
the harmonic coproduct to the new coproduct. We compute the new
coproduct in terms of an explicit coproduct of a suitable subalgebra
of the algebra of the free group with two generators.

The proof relies on an interpretation of the harmonic coproduct in terms of infinitesimal braid Lie algebras, which is implicit in the unpublished work of Deligne and Terasoma from 2005.