On deformed preprojective algebras
On deformed preprojective algebras
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DOI：
10.1016/j.jpaa.2022.107130
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发表时间：
2021-08
影响因子：
0.8
通讯作者：
W. Crawley-Boevey;Y. Kimura
中科院分区：
文献类型：
--
作者：
W. Crawley-Boevey;Y. Kimura
变形预投影代数是 Crawley-Boevey 和 Holland 引入的常见预投影代数的推广，可应用于 Kleinian 奇点、Deligne-Simpson 问题、可积系统和非交换几何。在本文中，我们为此类代数的研究提供了三个贡献：（1）2-Calabi-Yau 性质； (2) Crawley-Boevey 和 Holland 的反射函子与通常的预投影代数的反射函子的统一； (3) 2-Calabi-Yau 代数中倾斜理想的分类，特别是扩展 Dynkin 颤动的变形预投影代数中的倾斜理想分类。
Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.