The lie coalgebra of multiple polylogarithms - Greenberg, Zachary; Kaufman, Dani; Li, Haoran; Zickert, Christian K. (Journal of algebra, 2024)
We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, which we think of as functional relations for multiple polylogarithms. In particular, we have inversion relations and shuffle relations. We relate our definition to Goncharov's Bloch groups, and to the concrete model for L(F)≤4 by Goncharov and Rudenko.