Article Dans Une Revue International Mathematics Research Notices Année : 2018

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).

Fichier principal
Vignette du fichier
EF0 - Copie.pdf (298.08 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-03516990 , version 1 (07-01-2022)

Licence

Identifiants

Citer

Benjamin Enriquez, Hidekazu Furusho. A stabilizer interpretation of double shuffle Lie algebras. International Mathematics Research Notices, 2018, 2018 (22), pp.6870-6907. ⟨10.1093/imrn/rnx084⟩. ⟨hal-03516990⟩
42 Consultations
244 Téléchargements

Altmetric

Partager

  • More