Journal of Lie Theory

no. 1
On the Poisson Bracket on the Free Lie Algebra in two Generators
Journal of Lie Theory, Volume 16 (2006) no. 1, pp. 19-37
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.
DOI: 10.5802/jolt.394
Classification: 17B63, 17B70, 11F11
Keywords: Poisson bracket, graded Lie algebras, modular forms 
@article{JOLT_2006_16_1_a1,
     author = {L. Schneps},
     title = {On the {Poisson} {Bracket} on the {Free} {Lie} {Algebra} in two {Generators}},
     journal = {Journal of Lie Theory},
     pages = {19--37},
     year = {2006},
     volume = {16},
     number = {1},
     doi = {10.5802/jolt.394},
     zbl = {1120.17004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.394/}
}
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L. Schneps. On the Poisson Bracket on the Free Lie Algebra in two Generators. Journal of Lie Theory, Volume 16 (2006) no. 1, pp. 19-37. doi: 10.5802/jolt.394

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