A stabilizer interpretation of the (extended) linearized double shuffle Lie algebra

TL;DR

This paper provides a stabilizer interpretation of the extended linearized double shuffle Lie algebra, connecting it to multiple zeta values, q-zeta values, and Eisenstein series, and demonstrating the preservation of structure through stabilizers.

Contribution

It introduces a stabilizer perspective for both the original and extended linearized double shuffle Lie algebras, extending previous interpretations to new algebraic structures.

Findings

Stabilizers preserve the extended Lie algebra structure.

The interpretation links multiple zeta and Eisenstein series.

Extension maintains algebraic properties through stabilizers.

Abstract

The linearized double shuffle Lie algebra introduced by Brown reflects the depth-graded structure of multiple zeta values. In a previous paper, the first author introduced an extension of this Lie algebra that accommodates multiple q-zeta values and multiple Eisenstein series. Inspired by the stabilizer interpretation of the double shuffle Lie algebra given by Enriquez and Furusho, we provide in this paper a stabilizer interpretation of both Lie algebras and show that the stabilizers preserve the extension from the first linearized Lie algebra to the second one.