Geometric interpretation of double shuffle relation for multiple\n L-values

2010/12/22 by Hidekazu Furusho, Furusho, Hidekazu
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1012.4911

openalex publication_date 2010/12/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

Related

• A proof of the extended double shuffle relation without using integrals
• Some relations deduced from regularized double shuffle relations of multiple zeta values
• An alternative ℚ-form of the cyclotomic double shuffle Lie algebra
• On generic double shuffle relations, localized multiple polylogarithms and algebraic functions
• The double shuffle relations for p-adic multiple zeta values