On rational Drinfeld associators

Abstract

We prove an estimate on denominators of rational Drinfeld associators. To obtain this result, we prove the corresponding estimate for the p-adic associators stable under the action of suitable elements of \({{\rm Gal}(\bar{\mathbb{Q}}/\mathbb{Q})}\) . As an application, we settle in the positive Duflo’s question on the Kashiwara–Vergne factorizations of the Jacobson element J p (x, y) = (x + y)p − x p − y p in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant.