
Journal of Lie Theory 27 (2017), No. 2, 501528 Copyright Heldermann Verlag 2017 On the Irrationality of Certain Coefficients of the AlekseevTorossian Associator Matteo Felder Dept. of Mathematics, University of Geneva, 24 rue du Lièvre, 1211 Geneva 4, Switzerland Matteo.Felder@unige.ch We give explicit formulas for the first few coefficients of the AlekseevTorossian associator and a second Drinfeld associator defined by C. Rossi and T. Willwacher. This is done by analyzing the free and transitive action of the GrothendieckTeichmüller group and its Lie algebra grt_{1} on the set of Drinfeld associators. As a result we obtain that, up to a conjecture on multiple zeta values, both associators are not rational. Keywords: Drinfeld associators, GrothendieckTeichmueller group, GrothendieckTeichmueller Lie algebra, multiple zeta values. MSC: 17B01, 81R10 [ Fulltextpdf (421 KB)] for subscribers only. 