Geodesic
On the Poisson Bracket on the Free Lie Algebra in two Generators
Journal of Lie theory, Tome 16 (2006) no. 1, pp. 019-037.

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove a combinatorial formula for the Poisson bracket of two elements of the free Lie algebra on two generators, which has a particularly nice cocycle form when the two elements are Lie monomials containing only one y. By relating this cocycle form with the period polynomials introduced by Eichler-Shimura and Zagier, we completely describe and classify a set of fundamental relations in Ihara's stable derivation algebra, generalizing the first few cases of these relations which he had observed and computed by hand.
Classification : 17B63, 17B70, 11F11
Mots-clés : Poisson bracket, graded Lie algebras, modular forms 
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L. Schneps . On the Poisson Bracket on the Free Lie Algebra in two Generators. Journal of Lie theory, Tome 16 (2006) no. 1, pp. 019-037. http://geodesic.mathdoc.fr/item/JLT_2006_16_1_JLT_2006_16_1_a1/