The lie coalgebra of multiple polylogarithms
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 s...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 May 2024
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| In: |
Journal of algebra
Year: 2024, Volume: 645, Pages: 164-182 |
| ISSN: | 1090-266X |
| DOI: | 10.1016/j.jalgebra.2024.01.030 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jalgebra.2024.01.030 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0021869324000565 
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| Author Notes: | Zachary Greenberg, Dani Kaufman, Haoran Li, Christian K. Zickert |
| Summary: | 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. |
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| Item Description: | Online verfügbar 10 February 2024, Version des Artikels 19 February 2024 Gesehen am 23.09.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1090-266X |
| DOI: | 10.1016/j.jalgebra.2024.01.030 |