Relations between elliptic multiple zeta values and a special derivation algebra

TL;DR

This paper explores the relationship between elliptic multiple zeta values and a special derivation algebra, providing a method to count indecomposable elements and revealing new algebraic relations.

Contribution

It introduces a novel approach linking elliptic multiple zeta values to a derivation algebra, enabling enumeration of indecomposables and discovery of new algebraic relations.

Findings

Method to derive the number of indecomposable elements

Representation of elliptic multiple zeta values as iterated integrals over Eisenstein series

New relations in the derivation algebra

Abstract

We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for elliptic multiple zeta values and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for elliptic multiple zeta values over a wide range of weights and lengths.