On rational Drinfeld associators

摘要

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 (Q?/Q). As an application, we settle in the positive Duflo's question on the Kashiwara-Vergne factorizations of the Jacobson element Jp(x, y) = (x + y)p - xp - yp in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant.