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math.KT2022
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that t…
math.KT2022
The Lie coalgebra of multiple polylogarithms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
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, whic…