Symmetry, Integrability and Geometry: Methods and Applications (Nov 2006)
A Formula for the Logarithm of the KZ Associator
Abstract
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).