Title: Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras Show Chinese title

Title: 偏 perverse schobers，稳定性条件与二次微分 II：相对分级Brauer图代数

Abstract: We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calabi--Yau structure. We discovered these algebras through two very distinct routes, one involving perverse schobers whose stalks are cyclic quotients of the derived categories of relative Ginzburg algebras, and another involving deformations of partially wrapped Fukaya categories of surfaces. Applying the results of our previous work arXiv:2303.18249, we describe the spaces of stability conditions on the derived categories of these algebras in terms of spaces of quadratic differentials. Show Chinese abstract

Abstract: 我们引入了一类 dg-代数，它推广了经典的 Brauer 图代数。这些代数是从曲面的混合角剖分构造而来，并且通常具有（相对）Calabi–Yau 结构。我们通过两条非常不同的路径发现了这些代数：一条路径涉及其纤维为相对 Ginzburg 代数导出范畴的循环商的病态 Schober；另一条路径则涉及曲面的部分缠绕 Fukaya 范畴的形变。利用我们之前的工作 arXiv:2303.18249 的结果，我们用二次微分的空间来描述这些代数导出范畴上的稳定性条件空间。