论文标题
霍尔型代数用于分类唐纳森 - 托马斯理论的本地表面
Hall-type algebras for categorical Donaldson-Thomas theories on local surfaces
论文作者
论文摘要
我们表明，Porta-Sala在作者上一篇论文中引入的本地表面上的Porta-Sala构建的表面上的共同学厅代数结构降低了唐纳森 - 托马斯类别的那些。一个类似的论点还表明，局部表面上的pandharipande-thomas类别允许对表面上的零尺寸滑轮分类COHA的作用。我们还构建了其简单操作员的歼灭者的动作，并表明他们在K理论中的换向者满足与Weyl代数类似的关系。该结果可能被视为对由于Rennemo引起的局部平面曲线的Hilbert方案的Weyl代数作用的分类，这与Gopakumar-Vafa的生成一系列PT不变性的公式有关。
We show that the categorified cohomological Hall algebra structures on surfaces constructed by Porta-Sala descend to those on Donaldson-Thomas categories on local surfaces introduced in the author's previous paper. A similar argument also shows that Pandharipande-Thomas categories on local surfaces admit actions of categorified COHA for zero dimensional sheaves on surfaces. We also construct annihilator actions of its simple operators, and show that their commutator in the K-theory satisfies the relation similar to the one of Weyl algebras. This result may be regarded as a categorification of Weyl algebra action on homologies of Hilbert schemes of points on locally planar curves due to Rennemo, which is relevant for Gopakumar-Vafa formula of generating series of PT invariants.
