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Journal of Lie Theory 27 (2017), No. 2, 501--528
Copyright Heldermann Verlag 2017

On the Irrationality of Certain Coefficients of the Alekseev-Torossian Associator

Matteo Felder
Dept. of Mathematics, University of Geneva, 2-4 rue du Lièvre, 1211 Geneva 4, Switzerland

We give explicit formulas for the first few coefficients of the Alekseev-Torossian 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 Grothendieck-Teichmüller group and its Lie algebra grt1 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, Grothendieck-Teichmueller group, Grothendieck-Teichmueller Lie algebra, multiple zeta values.

MSC: 17B01, 81R10

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