Geometric interpretation of double shuffle relation for multiple L-values

Details Geometric interpretation of double shuffle relation for multiple L-values Geometric interpretation of double shuffle relation for multiple L-values

2010-12-22

arxiv.org/abs/1012.4911v2

Mathematics

Algebraic Geometry

19 pages

Scientific paper

This paper gives a geometric interpretation of the generalized (including the regularization relation) double shuffle relation for multiple $L$-values. Precisely it is proved that Enriquez' mixed pentagon equation implies the relations. As a corollary, an embedding from his cyclotomic analogue of the Grothendieck-Teichmuller group into Racinet's cyclotomic double shuffle group is obtained. It cyclotomically extends the result of our previous paper and the project of Deligne and Terasoma which are the special case N=1 of our result.

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