3 problems

Fix a Serre subcategory $\mathcal{S}$, a stability condition $\upzeta$, and a slope $\uptheta$. Let $\operatorname{\mathcal{S}ta}^{G,\upzeta}_{\Pi_Q,\uptheta}$ be the direct sum of…

Fix a quiver $Q$, a Serre subcategory $\mathcal{S}$, and a dimension vector $\mathbf{d}$ for which a simple $\mathbf{d}$-dimensional $\Pi_Q$-module exists. Let…

Let $Q$ be a quiver, let $\Pi_Q$ be its preprojective algebra, and let $\mathfrak{g}_{\Pi_Q}$ be the associated cohomologically graded BPS Lie algebra. Its grading is by dimension…