On the irrationality of certain coefficients of the Alekseev-Torossian associator

Abstract

We give explicit formulas for the first few coefficients of the Alekseev-Torossian associator and a second Drinfeld associator. This is done by analyzing the free and transitive action of the Grothendieck-Teichmüller group and its Lie algebra ${\mathfrak{grt}}_1$ 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.

arXiv comment24 pages

References in corpus (1)

• P. Etingof's conjecture about Drinfeld associators