论文标题
$ \ mathbb {C}^3 $（第二部分）的分类和K理论Donaldson-Thomas理论
Categorical and K-theoretic Donaldson-Thomas theory of $\mathbb{C}^3$ (part II)
论文作者
论文摘要
准BPS类别在三维仿射空间中的Hilbert方案的DT类别的半双胞胎分解中显示为汇总，以及在两个维仿射空间的分类霍尔代数中。在本文中，我们证明了类似于BPS皮带的类别类别的几种特性。 我们首先证明了Davison的支持引理的分类类似物，即，在三维仿射空间的对称产品中，在小的副产物中支持了准BPS类别中的复合物。分类支撑引理用于确定副本长度和重量的准BPS类别的圆环k理论的无扭转发生器。 接下来，我们在固定的长度和重量比例的Quasi-BPS类别的无扭转型k理论上构造了双gebra结构。我们将K理论的BPS空间定义为相对于共同点的原始元素的空间。我们表明，所有局部的模棱两可的k理论BPS空间都是一维的，这是三维仿射空间（数值）BPS不变的计算的K理论类似物。
Quasi-BPS categories appear as summands in semiorthogonal decompositions of DT categories for Hilbert schemes of points in the three dimensional affine space and in the categorical Hall algebra of the two dimensional affine space. In this paper, we prove several properties of quasi-BPS categories analogous to BPS sheaves in cohomological DT theory. We first prove a categorical analogue of Davison's support lemma, namely that complexes in the quasi-BPS categories for coprime length and weight are supported over the small diagonal in the symmetric product of the three dimensional affine space. The categorical support lemma is used to determine the torsion-free generator of the torus equivariant K-theory of the quasi-BPS category of coprime length and weight. We next construct a bialgebra structure on the torsion free equivariant K-theory of quasi-BPS categories for a fixed ratio of length and weight. We define the K-theoretic BPS space as the space of primitive elements with respect to the coproduct. We show that all localized equivariant K-theoretic BPS spaces are one dimensional, which is a K-theoretic analogue of the computation of (numerical) BPS invariants of the three dimensional affine space.
