7 problems

Let $Q$ be a quiver, let $\mathbf{d}$ be a dimension vector, and let $C_{Q,\mathbf{d}}^{\mathrm{abs}}(t)$ be the polynomial obtained from the graded Borcherds-algebra construction…

Let ${\mathfrak{e}}_{10}$ be the hyperbolic Kac–Moody algebra, and let $\mathcal{U}_{2}^{{\mathbbm{Z}}_{n}}$ be the automorphism defining the orbifold action. Let…

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…

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…

Let $Q$ be a quiver, let $\bar{\mathfrak{n}}_Q$ be the graded BPS Lie algebra arising from the filtration on $H_*(T^*\mathcal{M}_Q)$, and let $\widetilde{\mathfrak{n}}_Q$ be the po…

Comparison conjecture. The $\mathbb{Z}$-graded Lie algebras $\mathbf{g}_Q$ and $\widetilde{\mathfrak{g}}_Q$ are isomorphic.

Conjecture. If