The answer to this question may be well-known, but I failed to locate it in any obvious source. From the results of Bott (Ann. Math. 66 (1957), 203-248) and Kostant (Ann. Math. 74 (1961), 329-387), it follows that for the maximal nilpotent subalgebra $\mathfrak{n}$ of a complex semisimple Lie algebra $\mathfrak{g}$, one has an isomorphism of graded vector spaces $$ H^\bullet(\mathfrak{n},\mathbb{C})\cong H^{2\bullet}(G/B,\mathbb{C}) $$ of the Lie algebra cohomology of $\mathfrak{n}$ with constant coefficients and the cohomology of the corresponding flag variety $G/B$. However, this isomorphism multiplies degrees by two, and so cannot have anything to do with the multiplicative structure of the cohomology. My question is:

What is the (super-commutative) algebra structure of $H^\bullet(\mathfrak{n},\mathbb{C})$?

Even though I feel like it might be useful to state this question in full generality, I should probably say that I am mostly interested in the case $\mathfrak{g}=\mathfrak{sl}_{n}$, so that $\mathfrak{n}$ is the Lie algebra of all strictly upper-triangular matrices, and I ideally want the description to be by generators and relations.