6 papers
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…
A relation between Turaev coaction, Goncharov--Brown coaction and the reduced coaction Lie algebra
Muze Ren
We present a formula that relates the Turaev coaction and the Goncharov-Brown coaction. Motivated by this relation, we introduce the reduced coaction equation. The skew-symmetric s…
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…
Quantum Groups for Restricted SOS Models
Giovanni Felder, Muze Ren
We introduce the notion of restricted dynamical quantum groups through their category of representations, which are monoidal categories with a forgetful functor to the category of…