Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures

2025/08/11 by Florian Naef, Thomas Willwacher, Naef, Florian +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2508.08081

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra
• Depth-graded motivic multiple zeta values
• Double Shuffle and Kashiwara-Vergne Lie algebras
• Four groups related to associators
• The Kashiwara-Vergne conjecture and Drinfeld's associators

Cited by

• The 11-loop graph cohomology

Related

• On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra
• Divergence and q-divergence in depth 2
• Kashiwara-Vergne solutions degree by degree
• On the Jacobson element and generators of the Lie algebra \mathfrakgrt in nonzero characteristic
• Relating depth graded and block graded motivic Lie algebras