Deligne–Ihara freeness conjecture for the stable derivation algebra

Let $\mathfrak D_\bullet=\bigoplus_{w>2}\mathfrak D_w$ be the stable derivation algebra, a filtered graded Lie algebra over $\mathbb Q$. The conjecture concerns its generators in the grading by degree. Deligne–Ihara freeness conjecture. $\mathfrak D_\bullet$ is a free Lie algebra generated by one element in each degree $m=3,5,7,\ldots$. This structural conjecture supplies the expected dimensions used in the dimension bounds for the multiple zeta value algebra; the source attributes the relevant standard conjectures to Ihara and Deligne.