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The decomposition relations alone present the Goncharov Lie coalgebra
Abstract
Recently, Kupers--Rudenko--Sierra introduced the Goncharov Lie coalgebra. They gave a presentation using correlator generators and four types of relations: homogeneity, cyclic symmetry, shuffle relations, and decomposition relations. We show that the first three families of relations follow from the decomposition relations.
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BibTeX
@misc{aoki2026decomposition,
title = {{The decomposition relations alone present the Goncharov Lie coalgebra}},
author = {Ko Aoki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02307},
eprint = {2609.02307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02307},
}
RIS
TY - UNPB
TI - The decomposition relations alone present the Goncharov Lie coalgebra
AU - Ko Aoki
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02307
UR - https://arxiv.org/abs/2609.02307
AB - Recently, Kupers--Rudenko--Sierra introduced the Goncharov Lie coalgebra. They gave a presentation using correlator generators and four types of relations: homogeneity, cyclic symmetry, shuffle relations, and decomposition relations. We show that the first three families of relations follow from the decomposition relations.
ER -