The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913800967421952 |
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| author | Schneps, Leila |
| author_facet | Schneps, Leila |
| contents | In this article we prove that there exists an injective Lie morphism from the double shuffle Lie algebra ${\frak{ds}}$ into the Kashiwara-Vergne Lie algebra ${\frak{krv}}$, forming a commutative triangle with the known Lie injections of the Grothendieck-Teichmüller Lie algebra ${\frak{grt}}\rightarrow {\frak{ds}}$ and ${\frak{grt}}\rightarrow{\frak{krv}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra Schneps, Leila Rings and Algebras 17B37 17B70 In this article we prove that there exists an injective Lie morphism from the double shuffle Lie algebra ${\frak{ds}}$ into the Kashiwara-Vergne Lie algebra ${\frak{krv}}$, forming a commutative triangle with the known Lie injections of the Grothendieck-Teichmüller Lie algebra ${\frak{grt}}\rightarrow {\frak{ds}}$ and ${\frak{grt}}\rightarrow{\frak{krv}}$. |
| title | The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra |
| topic | Rings and Algebras 17B37 17B70 |
| url | https://arxiv.org/abs/2504.14293 |