Here is a connection that I recently noticed, but I haven't quite been able to make sense of. It might follow from well-known facts; apologies, if so. This is quite far from my area. First, in ["Yang-Mills Algebra", arXiv:0206205](https://arxiv.org/pdf/math/0206205.pdf) by Connes and Dubois-Violette, they construct the Yang-Mills algebra $\mathcal{A}$ and study some of its properties. On p. 7, they mention that $\mathcal{A}$ is the universal enveloping algebra of a certain graded Lie algebra $\bigoplus_{j \geq 1} \mathfrak{g}_j$, and give an explicit formula for the dimensions, which begins: $$ 4, \mathbf{6}, 16, 45, 144, 440, \dots $$ This is sequence [A072279](https://oeis.org/A072279) (In fact, I think the bold **6** in their paper and the OEIS entry is a typo, as their own formula yields 5). EDIT: No, as @DamienC points out, it seems as if the 6 is correct. Second, I was recently looking at the ranks of the lower central factors of the surface group $S_2 = \langle a, b, c, d \mid [a,b][c,d]=1 \rangle$, i.e. the factor groups in the lower central series of $S_2$. Curiously, I noticed that this is given by the same formula as in the case above (though with a 5 instead of a 6). There are known ways to get there in high-powered ways, as e.g. in [this answer](https://mathoverflow.net/a/279162/120914) using Koszul duality (which I do not understand). Furthermore, [this question](https://mathoverflow.net/questions/302250/quotient-groups-of-the-lower-central-series-of-a-surface-group) and the answer to it are of course relevant, especially given the paper linked in there by Papadima and Yuzvinsky. So I suppose everything on this side seems fairly well understood. My question is then: **Q. Is there a deeper connection between surface groups and the (Lie algebra associated to the) Yang-Mills algebra $\mathcal{A}$**? Of course, the answer might be "no, the dimensions just satisfy the same relation", or "yes, by general facts about Koszul algebras", either of which I suppose I would be satisfied with, too. I've added the [tag:reference-request] tag, just in case.