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

摘要

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-Teichmuller 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.