Minimal model of a wedge of simply connected spheres

For a finite wedge sum of spheres of dimensions $n_i\ge 2$, let $L=\mathbb{L}(e_i)$ with $|e_i|=n_i-1$ and zero differential. Its Chevalley–Eilenberg cochains of a graded Lie algebra are a minimal commutative differential graded algebra: one generator dual to each Lie basis word has degree one more than that word, and its differential is dual to the Lie bracket. Its cohomology is $\mathbb{Q}\oplus {⨁}_i\mathbb{Q}{a}_{n_i}$ with all positive products zero. One way to compute this is $U(L)=T(e_i)$; the augmentation module has a length-one free resolution, so the corresponding Ext has only the unit and the dual generating classes.