2 problems

Let $\mathcal A$ and $\mathcal B$ be hereditary abelian categories. Their root categories are the orbit categories $\mathcal D^b(\mathcal A)/[2]$ and $\mathcal D^b(\mathcal B)/[2]$…

Peng–Xiao's conjecture. The desired enlargement of the Hall algebra, recovering the full quantum enveloping algebra $U_q(\mathfrak g)$ rather than only its positive Borel part, sho…