A stabilizer interpretation of double shuffle Lie algebras
Résumé
According to Racinet's work, the scheme of double shuffle and regularization relations between cyclotomic analogues of multiple zeta values has the structure of a torsor over a pro-unipotent Q-algebraic group DMR0, which is an algebraic subgroup of a pro-unipotent Q-algebraic group of outer automorphisms of a free Lie algebra. We show that the harmonic (stuffle) coproduct of double shuffle theory may be viewed as an element of a module over the above group, and that DMR0 identifies with the stabilizer of this element. We identify the tangent space at origin of DMR0 with the stabilizer Lie algebra of the harmonic coproduct, thereby obtaining an alternative proof of Racinet's result stating that this space is a Lie algebra (the double shuffle Lie algebra).
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