论文标题
异常等价和DG稳定组合学
Perverse Equivalences and Dg-stable Combinatorics
论文作者
论文摘要
Chuang and Rouquier描述了在Calabi-yau尺寸$ -1 $的三角类别类别的基础基础上，通过不正当等价的行动。我们为Calabi-yau dimension $ W <0 $的Calabi-yau类别开发了一个类似物，并表明它等同于$ w $ simple的系统的突变理论。 鉴于非物性分级，有限维对称代数$ a $ a $，我们表明$ a $ a $的差分级稳定类别具有负Calabi-yau尺寸。当$ a $是brauer树代数时，我们构建了DG稳定类别的组合模型，并表明，不正当等价在$ | w | $ -bases的集合上进行了固定作用。
Chuang and Rouquier describe an action by perverse equivalences on the set of bases of a triangulated category of Calabi-Yau dimension $-1$. We develop an analogue of their theory for Calabi-Yau categories of dimension $w<0$ and show it is equivalent to the mutation theory of $w$-simple-minded systems. Given a non-positively graded, finite-dimensional symmetric algebra $A$, we show that the differential graded stable category of $A$ has negative Calabi-Yau dimension. When $A$ is a Brauer tree algebra, we construct a combinatorial model of the dg-stable category and show that perverse equivalences act transitively on the set of $|w|$-bases.
