论文标题
箭袋的单位包围代数的几何实现
Geometric realisations of the unipotent enveloping algebra of a quiver
论文作者
论文摘要
我们将各种几何构建体（由于林德，卢斯蒂格，斯科菲尔德，博兹克，戴维森...）与与任意颤动相关的一般广义kac-moody代数。这些结构通过多个几何操作互连，包括构造络合物的茎欧特征，特征周期，欧拉障碍物图和拉格朗日亚变量的相交多重性。我们提供了证明这些几何实现对谎言代数的整体形式所持有的。此外，通过修改包围代数的发电机，我们确保与可以根据限制图来定义的自然相关性兼容。 结果，我们确定严格的静态堆栈的最高共同体大厅代数是与Quiver相关的广义KAC-MOODY代数的封闭代数的正面部分。这似乎是描述非常通用的$ 2 $ -Calabi-yau类别的BPS代数所需的基石之一，这是作者在BPS Lie代数上工作的主题，以$ 2 $ -Calabi-yau类别与Davison和Schlegel Mejia。
We compare and generalise the various geometric constructions (due to Ringel, Lusztig, Schofield, Bozec, Davison...) of the unipotent generalised Kac-Moody algebra associated with an arbitrary quiver. These constructions are interconnected through several geometric operations, including the stalk Euler characteristic of constructible complexes, the characteristic cycle, the Euler obstruction map, and the intersection multiplicities of Lagrangian subvarieties. We provide a proof that these geometric realisations hold for the integral form of the Lie algebra. Furthermore, by modifying the generators of the enveloping algebra, we ensure compatibility with the natural coproducts that can be defined in terms of restriction diagrams. As a result, we establish that the top cohomological Hall algebra of the strictly seminilpotent stack is isomorphic to the positive part of the enveloping algebra of the generalised Kac-Moody algebra associated with the quiver. This appears to be one of the cornerstones needed to describe the BPS algebra of very general $2$-Calabi-Yau categories, which is the subject of the author's work on BPS Lie algebras for $2$-Calabi-Yau categories with Davison and Schlegel Mejia.
