标题： 某些环柄奇点产生的高阶遗传代数和卡拉比-丘代数 显示英文标题

标题： Higher hereditary algebras and Calabi-Yau algebras arising from some toric singularities

摘要： 我们研究了一些交换Gorenstein的toric奇点的分次和非分次奇异范畴，即多项式环的Veronese子环，以及一些多项式环的Segre乘积。 我们证明分次奇异范畴有一个tilting对象，其自同态环是更高表示无限的。 此外，我们构造了这个tilting对象，使得其自同态环具有更高Auslander-Reiten转换的严格根对，这使我们能够以一种方式在奇异范畴和（折叠的）cluster范畴之间给出等价，使得它们的cluster tilting对象相互对应。 我们tilting对象的特殊形式也允许我们构造（扭曲的）Calabi-Yau代数，作为根对的Calabi-Yau完成。 我们给出了这些扭曲的Calabi-Yau代数以及更高表示无限代数的显式描述，包括它们的quiver和关系。 在此过程中，我们证明了某些更高表示无限代数的幂等商仍然保持更高表示无限。 显示英文摘要

摘要： We study graded and ungraded singularity categories of some commutative Gorenstein toric singularities, namely, Veronese subrings of polynomial rings, and Segre products of some copies of polynomial rings. We show that the graded singularity category has a tilting object whose endomorphism ring is higher representation infinite. Moreover, we construct the tilting object so that the endomorphism ring has a strict root pair of its higher Auslander-Reiten translation, which allows us to give equivalences between singularity categories and (folded) cluster categories in a such a way that their cluster tilting objects correspond to each other. Our distinguished form of tilting objects also allows us to construct (twisted) Calabi-Yau algebras as the Calabi-Yau completions of the root pairs. We give an explicit description of these twisted Calabi-Yau algebras as well as the higher representation infinite algebras in terms of quivers and relations. Along the way, we prove that certain idempotent quotients of higher representation infinite algebras remain higher representation infinite.