ScalingStacks

Remark 3.1.5. Note that the algebra $H^{\mathrm{nil}}(W)$ is acyclic if $S\neq\emptyset$.

Note also that one can introduce a family of commuting differentials $d_{s}$ for $s\in S$ modulo conjugacy by setting $d_{s}(T_{t})=1$ if $t\in S$ is conjugate to $s$ and $d_{s}(T_{t})=0$ otherwise.