Double shuffle and Kashiwara-Vergne Lie algebras

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We prove that the double shuffle Lie algebra ds, dual to the space of new formal multiple zeta values, injects into the Kashiwara-Vergne Lie algebra krv2 defined and studied by Alekseev and Torossian. The proof is based on a reformulation of the definition of krv2, and uses a theorem of Ecalle on a property of elements of ds. In the final section, we lift this result to an injection DS{right arrow, hooked}KRV 2 of the corresponding pro-unipotent groups. © 2012 Elsevier Inc.




Schneps, L. (2012). Double shuffle and Kashiwara-Vergne Lie algebras. Journal of Algebra, 367, 54–74.

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