To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these algebras and then use the structure of an associated hyperplane arrangement to control the compositions, obtaining a faithful group action on the bounded derived category. Further, we determine precisely those standard equivalences which are induced by two-term tilting complexes and show that any standard equivalence between contraction algebras (up to algebra automorphism) can be viewed as the composition of our constructed functors. Thus, for a contraction algebra, we obtain a complete picture of its derived equivalence class and, in particular, of its derived autoequivalence group.

中文翻译：

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收缩代数的倾斜理论

Donovan-Wemyss 将一个完整的局部孤立 cDV 奇点的每个最小模型关联到一个有限维对称代数，称为收缩代数。我们在这些代数之间构建了第一个已知的标准派生等价，然后使用相关超平面排列的结构来控制组合，在有界派生类别上获得忠实的群作用。此外，我们精确地确定了那些由两项倾斜复形引起的标准等价，并表明收缩代数（直到代数自同构）之间的任何标准等价都可以被视为我们构造的函子的组合。因此，对于收缩代数，我们获得了其派生等价类的完整图片，特别是其派生自等价群的完整图片。