On free generators in the Grothendieck-Teichmüller Lie Algebra

Abstract

We prove that any homogeneous family $σ_3,σ_5,\ldots$ in $\mathfrak{grt}_1(\mathbb K)$ with nonzero coefficients of $x^{2k}y$ in $σ_{2k+1}$ generates a free Lie subalgebra, building on the work of Brown.

Disclosure

“was dicussed with the AI, on the basis of making my old lecture notes on Brown’s work into a paper, with the upgrade of replacing the role of the KZ associator in those notes by a more general one. After the exact plan was decided, I used ChatGPT 5.6 Pro to generate a first draft of the paper on the basis of the lecture notes, which was then iteratively improved in several rounds of prompting. Once this resulted in a somewhat acceptable text, I took over the editing and revised and”

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Classification

Drafting limited passages

Multiplier

5

Verified

2026-08-23T18:59:49.897333Z

Structural counts