Dihedral symmetries of multiple logarithms

Abstract

This paper finds relationships between multiple logarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin's R-deco polygon representation of multiple logarithms to find these relations. By writing multiple logarithms as iterated integrals, my arguments are valid for iterated integrals as over an arbitrary field.

References in corpus (4)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• Multiple polylogarithms and mixed Tate motives
• Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
• Galois symmetries of fundamental groupoids and noncommutative geometry