2 problems

Let $\mathfrak{a}$ be a graded Lie algebra with two generators, and let $\mathfrak{g}$ be a reductive Lie algebra with invariant algebra $\operatorname{Sym}(\mathfrak{g}^*)^G$. If…

Let $W$ be a $k$-vector space with $\dim W=2$, let $A=\operatorname{Sym}(W)$, and let $R$ be a minimal resolution of $A$. For each $n\geq 1$, let … be the map induced by the derive…