A Formula for the Logarithm of the KZ Associator
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formulaassociatorlogarithmalgebracertaincoincidesderiveelement
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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).
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