The Lie coalgebra of multiple polylogarithms

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

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

Harvard

Greenberg, Z, Kaufman, D, Li, H & Zickert, CK 2024, 'The Lie coalgebra of multiple polylogarithms', Journal of Algebra, vol. 645, pp. 164-182. https://doi.org/10.1016/j.jalgebra.2024.01.030

APA

Greenberg, Z., Kaufman, D., Li, H., & Zickert, C. K. (2024). The Lie coalgebra of multiple polylogarithms. Journal of Algebra, 645, 164-182. https://doi.org/10.1016/j.jalgebra.2024.01.030

Vancouver

Greenberg Z, Kaufman D, Li H, Zickert CK. The Lie coalgebra of multiple polylogarithms. Journal of Algebra. 2024;645:164-182. https://doi.org/10.1016/j.jalgebra.2024.01.030

Author

Greenberg, Zachary ; Kaufman, Dani ; Li, Haoran ; Zickert, Christian K. / The Lie coalgebra of multiple polylogarithms. In: Journal of Algebra. 2024 ; Vol. 645. pp. 164-182.

Bibtex

@article{333865a5ee6c4620867767139fbd09a9,
title = "The Lie coalgebra of multiple polylogarithms",
abstract = "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.",
keywords = "Bloch groups, Motivic Lie coalgebra, Multiple polylogarithms, Polylogarithm relations, Symbols",
author = "Zachary Greenberg and Dani Kaufman and Haoran Li and Zickert, {Christian K.}",
year = "2024",
doi = "10.1016/j.jalgebra.2024.01.030",
language = "English",
volume = "645",
pages = "164--182",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press",

}

RIS

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