Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916891380940800 |
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| author | Naef, Florian Willwacher, Thomas |
| author_facet | Naef, Florian Willwacher, Thomas |
| contents | We compute numerically the dimensions of the graded quotients of the linearized Kashiwara-Vergne Lie algebra lkv in low weight, confirming a conjecture of Raphael-Schneps in those weights. The Lie algebra lkv appears in a chain of inclusions of Lie algebras, including also the linearized double shuffle Lie algebra and the (depth associated graded of the) Grothendieck-Teichmüller Lie algebra. Hence our computations also allow us to check the validity of the Deligne-Drinfeld conjecture on the structure of the Grothendieck-Teichmüller group up to weight 29, and (a version of) the the Broadhurst-Kreimer conjecture on the number of multiple zeta values for a range of weight-depth pairs significantly exceeding the previous bounds. Our computations also verify a conjecture by Alekseev-Torossian on the Kashiwara-Vergne Lie algebra up to weight 29. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures Naef, Florian Willwacher, Thomas Quantum Algebra We compute numerically the dimensions of the graded quotients of the linearized Kashiwara-Vergne Lie algebra lkv in low weight, confirming a conjecture of Raphael-Schneps in those weights. The Lie algebra lkv appears in a chain of inclusions of Lie algebras, including also the linearized double shuffle Lie algebra and the (depth associated graded of the) Grothendieck-Teichmüller Lie algebra. Hence our computations also allow us to check the validity of the Deligne-Drinfeld conjecture on the structure of the Grothendieck-Teichmüller group up to weight 29, and (a version of) the the Broadhurst-Kreimer conjecture on the number of multiple zeta values for a range of weight-depth pairs significantly exceeding the previous bounds. Our computations also verify a conjecture by Alekseev-Torossian on the Kashiwara-Vergne Lie algebra up to weight 29. |
| title | Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2508.08081 |