4 papers · 1 filter
The kernel of formal polylogarithms
Anton Alekseev, Megan Howarth, Florian Naef +2
Polylogarithmic functions (polylogs) in variables can be viewed as elements of , the dual of the universal enveloping algebra of the Lie algebra $\mathfr…
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 is defined by a skew-symmetric condition together with an algebraic equation involving the reduced coaction, a non-cyclic refinem…
Poisson brackets and coaction maps of regularized holonomies of the KZ equation
Anton Alekseev, Florian Naef, Muze Ren
We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS) coaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov (KZ) equation, and the cor…
Generalized Pentagon Equations
Anton Alekseev, Florian Naef, Muze Ren
Drinfeld defined the Knizhinik--Zamolodchikov (KZ) associator by considering the regularized holonomy of the KZ connection along the {\em droit chemin} . The KZ…