Enriquez, Benjamin; Gavarini, Fabio A formula for the logarithm of the KZ associator. (English) Zbl 1188.17004 SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 080, 3 p. (2006). Summary: 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 Tu Quoc Thang and J. Murakami [Nagoya Math. J. 142, 39–65 (1996; Zbl 0866.57008)] for the Knizhnik-Zamolodchikov (KZ) associator \(\Phi\) to derive a formula for \(\log\Phi\) in terms of MZV’s (multiple zeta values). Cited in 1 Document MSC: 17B01 Identities, free Lie (super)algebras 11M32 Multiple Dirichlet series and zeta functions and multizeta values 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain Keywords:free Lie algebras; Campbell-Baker-Hausdorff series, Knizhnik-Zamolodchikov associator Citations:Zbl 0866.57008 PDFBibTeX XMLCite \textit{B. Enriquez} and \textit{F. Gavarini}, SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 080, 3 p. (2006; Zbl 1188.17004) Full Text: DOI arXiv EuDML EMIS