Double shuffle relation for associators. (English) Zbl 1321.11088

Summary: It is proved that Drinfel’d’s pentagon equation implies the generalized double shuffle relation. As a corollary, an embedding from the Grothendieck-Teichmüller group \(\text{GRT}_1\) into Racinet’s double shuffle group \(\text{DMR}_0\) is obtained, which settles the project of Deligne-Terasoma. It is also proved that the gamma factorization formula follows from the generalized double shuffle relation.


11M32 Multiple Dirichlet series and zeta functions and multizeta values
14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
11G55 Polylogarithms and relations with \(K\)-theory
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
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