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 Gal(\bar{Q}/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.

16 pages; v2: new section on Kontsevich knot invariant; v3: new Theorem 3.1 on construction of associators out of elements of GT

References in corpus (4)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• The Kashiwara-Vergne conjecture and Drinfeld's associators
• Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations
• On the Jacobson element and generators of the Lie algebra $\mathfrak{grt}$ in nonzero characteristic