×

A formula for the logarithm of the KZ associator. (English) Zbl 1188.17004

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).

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

Citations:

Zbl 0866.57008
PDFBibTeX XMLCite
Full Text: DOI arXiv EuDML EMIS