Motivic double shuffle

TL;DR

This paper provides an elementary proof of the double shuffle relations for motivic multiple zeta values, utilizing a modified method for the stuffle relation originally introduced by Cartier, with implications for understanding their algebraic structure.

Contribution

It introduces a simplified proof of the double shuffle relations for motivic multiple zeta values, especially for the stuffle part, using a novel adaptation of Cartier's method.

Findings

Elementary proof of shuffle relations for motivic multiple zeta values

Modified Cartier method for proving stuffle relations

Clarification of algebraic structure of motivic multiple zeta values

Abstract

The goal of this article is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle we use a modification of a method first introduced by P. Cartier for the purpose of proving stuffle for the real multiple zeta values via integrals and blow-up sequences.