On the relation between Grothendieck-Teichmüller, double shuffle, and Kashiwara-Vergne Lie algebras - A. Alekseev

Mar 9, 2026  ·   In Kyoto Japan  ·   Event ``AHGT Seminar''

Abstract

The Grothendieck-Teichmüller (grt), double shuffle (dmr), and Kashiwara-Vergne (krv) Lie algebras encode universal infinitesimal symmetries of braided monoidal categories, of formal multiple zeta-values (MZVs), and of Lie algebras, respectively. They can all be realized as Lie subalgebras of derivations of the free Lie algebra with two generators, and conjecturally, they are all isomorphic to each other.

In the talk, we will recall definitions of these three Lie algebras, and we will review the status of isomorphism conjectures. In particular, we will state the fundamental result of Furusho on the injective Lie homomorphism from grt to dmr, on the injection of grt to krv, and a recent result by Enriquez-Furusho and Schneps on the injection of dmr to krv. We will also mention the results of Kuno and Ren on the emergent version of krv, and of Howarth-Ren, Enriquez-Furusho, and Markarian on characterization of dmr.

Erratum - rc_0 need the skew-symmetric condition.

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3. H. Furusho, Double shuffle relation for associators. Ann. of Math. (2) 174 (2011), no. 1, 341–360.
4. A. Alekseev and C. Torossian. Kashiwara-Vergne conjecture and Drinfeld's associators. Ann. of Math. (2) 175 (2012), no. 2, 415–463.