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math.QA2025
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…
math.RA2025
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…