4 problems

Let $Q$ be a quiver whose underlying unoriented graph is a disjoint union of Dynkin diagrams of type $A$, $D$, or $E$. A representation of $Q$ is called stable with respect to a we…

Let $Q$ be a Dynkin quiver, and let $k$ be the field over which its representations are taken. Write $\mathrm{\mathbf{Rep}}_k(Q)$ for the abelian category of finite-dimensional $k$…

Let $Q$ be a quiver of Dynkin type. A weight system $\Theta$ on $Q$ is understood in the sense of stability for representations of $Q$, and a representation is stable with respect…

Let $\Gamma$ be a quiver and let $\mathbf{k}$ be a field. Call $\Gamma$ $\mathbf{k}$-even if the complexes $\pi_{y*}\underline{\mathbf{k}}_{\widetilde{F}_{y}}$ are even for every…