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A Formula for the Logarithm of the KZ Associator
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\Phi$ to derive a formula for $\log(\Phi)$ in terms of MZV's (multiple zeta values).
Keywords: free Lie algebras; Campbell–Baker–Hausdorff series, Knizhnik–Zamolodchikov associator. 
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     author = {Benjamin Enriquez and Fabio Gavarini},
     title = {A~Formula for the {Logarithm} of the {KZ} {Associator}},
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}
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Benjamin Enriquez; Fabio Gavarini. A Formula for the Logarithm of the KZ Associator. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a79/

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