Benjamin Enriquez, Fabio Gavarini, “A Formula for the Logarithm of the KZ Associator”, SIGMA, 2006, Volume 2,080, 3 pp.

This article is cited in 2 papers

A Formula for the Logarithm of the KZ Associator

Benjamin Enriquez^a, Fabio Gavarini^b

^a IRMA (CNRS), rue René Descartes, F-67084 Strasbourg, France
^b Universitá degli Studi di Roma ''Tor Vergata'', Dipartimento di Matematica, Via della Ricerca Scientifica 1, I-00133 Rome, Italy

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 $\Phi$ 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.

MSC: 17B01; 81R50

Received: October 3, 2006; in final form November 10, 2006; Published online November 13, 2006

Language: English

DOI: 10.3842/SIGMA.2006.080