A formula for the logarithm of the KZ associator - Enriquez, B.; Gavarini, F. (Symmetry, Integrability and Geometry: Methods and Applications, 2006)
We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator Φ to derive a formula for log(Φ) in terms of MZV's (multiple zeta values).