Double shuffle relation for associators

Details Double shuffle relation for associators Double shuffle relation for associators

2008-08-03

arxiv.org/abs/0808.0319v3

Annals of Mathematics, Vol. 174 (2011), No. 1, 341-360

Mathematics

Algebraic Geometry

16 pages

Scientific paper

It is proved that Drinfel'd's pentagon equation implies the generalized double shuffle relation. As a corollary, an embedding from the Grothendieck-Teichm\"uller group $GRT_1$ into Racinet's double shuffle group $DMR_0$ 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.

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