Polylogarithmic characterizations of the reduced coaction Lie algebra and the double shuffle Lie algebra, and their relation to the Kashiwara--Vergne Lie algebra

Megan Howarth, Muze Ren

The reduced coaction Lie algebra ${\mathfrak{rc}}_0$ is defined by a skew-symmetric condition together with an algebraic equation involving the reduced coaction, a non-cyclic refinem…