5 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 $G$ be a reductive affine algebraic group over a field $k$ of characteristic zero, and let $\Sigma_g$ be a closed Riemann surface of genus $g\geq 1$. Write…

Let $\mathfrak{G}$ be the category of finitely generated free groups, let $D$ be a polynomial bifunctor on $\mathfrak{G}$, and let … be the stable trace map from stable automorphis…

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…

Let $E$ be a smooth commutative algebra, and let $\mathfrak{gl}_{\infty}(E)$ and $\mathfrak{gl}_n(E)$ be the infinite and finite general linear Lie algebras over $E$, with correspo…