The Lie coalgebra of multiple polylogarithms
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The Lie coalgebra of multiple polylogarithms. / Greenberg, Zachary; Kaufman, Dani; Li, Haoran; Zickert, Christian K.
In: Journal of Algebra, Vol. 645, 2024, p. 164-182.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Lie coalgebra of multiple polylogarithms
AU - Greenberg, Zachary
AU - Kaufman, Dani
AU - Li, Haoran
AU - Zickert, Christian K.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Bloch groups
KW - Motivic Lie coalgebra
KW - Multiple polylogarithms
KW - Polylogarithm relations
KW - Symbols
U2 - 10.1016/j.jalgebra.2024.01.030
DO - 10.1016/j.jalgebra.2024.01.030
M3 - Journal article
AN - SCOPUS:85185578158
VL - 645
SP - 164
EP - 182
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 384872146