论文标题
派生的澳大利亚 - iyama通信
The Derived Auslander-Iyama Correspondence
论文作者
论文摘要
我们在一个完美的领域工作。第三名作者的最新工作建立了一个衍生的Auslander信函，该信函将有限的自注释代数与有限的三角形类别类别扭曲了$ 3 $ periodic。此外，上述工作还表明，后者的三角类别承认了独特的差异分级增强。在本文中，我们证明了该结果的更高维度版本，鉴于整数$ d \ geq1 $，将扭曲的$（d+2）$ - 定期代数与代数三角形类别与$ d \ mathbb {z} $ - cluster tilting tilting对象。我们还表明，后者的三角类别承认了独特的差异分级增强。 Our result yields recognition theorems for interesting algebraic triangulated categories, such as the Amiot cluster category of a self-injective quiver with potential in the sense of Herschend and Iyama and, more generally, the Amiot-Guo-Keller cluster category associated with a $d$-representation finite algebra in the sense of Iyama and Oppermann.作为我们结果的应用，我们获得了无限的许多三角类别，具有独特的差分增强功能，并非非常独特。在附录中，凯勒（B. Keller）解释了我们的主要结果是如何与八月和瓦阿·卡勒（Whua-Keller）的关键结果结合在一起的，这是在同源最小模型计划的背景下，证明了Donovan-Wemyss猜想的最后一个关键要素。
We work over a perfect field. Recent work of the third-named author established a Derived Auslander Correspondence that relates finite-dimensional self-injective algebras that are twisted $3$-periodic to algebraic triangulated categories of finite type. Moreover, the aforementioned work also shows that the latter triangulated categories admit a unique differential graded enhancement. In this article we prove a higher-dimensional version of this result that, given an integer $d\geq1$, relates twisted $(d+2)$-periodic algebras to algebraic triangulated categories with a $d\mathbb{Z}$-cluster tilting object. We also show that the latter triangulated categories admit a unique differential graded enhancement. Our result yields recognition theorems for interesting algebraic triangulated categories, such as the Amiot cluster category of a self-injective quiver with potential in the sense of Herschend and Iyama and, more generally, the Amiot-Guo-Keller cluster category associated with a $d$-representation finite algebra in the sense of Iyama and Oppermann. As an application of our result, we obtain infinitely many triangulated categories with a unique differential graded enhancement that is not strongly unique. In the appendix, B. Keller explains how -- combined with crucial results of August and Hua-Keller -- our main result yields the last key ingredient to prove the Donovan-Wemyss Conjecture in the context of the Homological Minimal Model Program for threefolds.
