Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918245259280384 |
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| author | Howarth, Megan Ren, Muze |
| author_facet | Howarth, Megan Ren, Muze |
| contents | We study the reduced coaction Lie algebra $\mathfrak{rc}_0$, which is defined by an algebraic equation satisfied by the reduced coaction (an upgraded version of the necklace cobracket) and the skew-symmetric condition. We prove that the double shuffle Lie algebra $\mathfrak{dmr}_0$ together with the skew-symmetric condition injects to $\mathfrak{rc}_0$, and that $\mathfrak{rc}_0$ together with the krv1 equation injects to the Kashiwara-Vergne Lie algebra $\mathfrak{krv}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation Howarth, Megan Ren, Muze Quantum Algebra Number Theory We study the reduced coaction Lie algebra $\mathfrak{rc}_0$, which is defined by an algebraic equation satisfied by the reduced coaction (an upgraded version of the necklace cobracket) and the skew-symmetric condition. We prove that the double shuffle Lie algebra $\mathfrak{dmr}_0$ together with the skew-symmetric condition injects to $\mathfrak{rc}_0$, and that $\mathfrak{rc}_0$ together with the krv1 equation injects to the Kashiwara-Vergne Lie algebra $\mathfrak{krv}_2$. |
| title | Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation |
| topic | Quantum Algebra Number Theory |
| url | https://arxiv.org/abs/2509.20275 |