On free generators in the Grothendieck-Teichmüller Lie Algebra

Thomas Willwacher

On free generators in the Grothendieck-Teichmüller Lie Algebra

Quantum Algebra 2026-07-21 v1

Authors: Thomas Willwacher

Abstract

We prove that any homogeneous family $\sigma_3,\sigma_5,\ldots$ in $\mathfrak{grt}_1(\mathbb K)$ with nonzero coefficients of $x^{2k}y$ in $\sigma_{2k+1}$ generates a free Lie subalgebra, building on the work of Brown.

Keywords

Grothendieck-Teichmüller Lie algebra free Lie subalgebra homogeneous family generators

Cite

@article{arxiv.2607.18793,
  title  = {On free generators in the Grothendieck-Teichmüller Lie Algebra},
  author = {Thomas Willwacher},
  journal= {arXiv preprint arXiv:2607.18793},
  year   = {2026}
}