Tilting complex and Perverse equivalence in Representation theory

表示论中的倾斜复数与反常等价

• 批准号: 17F17814
• 负责人: 伊山 修
• 金额: $ 1.41万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2017
• 资助国家: 日本
• 起止时间: 2017-11-10 至 2020-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17F17814/
• 关键词: Homological algebra; triangulated category; Perverse Equivalence; Torsion class; Mutation; Preprojective algebra; Symmetric Group Representations; Okuyama tilting complex; homological algebra; DG module; silting theory; Serre subcategory; tors

With the help of the host we have investigate a type of perverse equivalence that correspond to two-term tilting. In general not all two-term tilting is a perverse equivalence. The condition of an algebra with all two-term tilting complex can be described using Jasso reduction. There is also an investigation into the particular case of preprojective algebra. In which we have determined the type of two-term tilting that is a perverse equivalence and related it to combinatorics of symmetric group.Also we have established a link between Rouquier-Okuyama tilting complex to perverse equivalence, as suggested at the start of the project. There are still a lot of questions remain unanswered but we managed to get the results we hoped for.Beside the above main progresses we have managed to conclude the work in homology of p-complexes of some symmetric group representations, a joint work with Aaron Chan in Nagoya University. The work with TUS is satisfactorily conducted.

在主持人的帮助下，我们研究了一种与两项倾斜相对应的反常等价。一般来说，并非所有的两项倾斜都是反常的等价。具有所有两项倾斜复形的代数的条件可以使用 Jasso 约简来描述。还对原射代数的特殊情况进行了研究。其中我们确定了作为反常等价的两项倾斜的类型，并将其与对称群的组合数学相关联。此外，正如项目开始时所建议的那样，我们还建立了 Rouquier-Okuyama 倾斜复形与反常等价之间的联系。虽然还有很多问题没有得到解答，但我们已经得到了我们希望的结果。除了上述主要进展之外，我们还成功完成了与 Aaron Chan 合作的一些对称群表示的 p 复合体的同源性工作在名古屋大学。与启迪的合作进展顺利。

项目成果

Homological Approach to Representations

表示的同调方法

• 发表时间: 2018
• 作者: Hon Yin Wong

Derived Equivalence and Perverse Equivalence

派生等价和反常等价

• 发表时间: 2019
• 作者: Hon Yin Wong

Perverse equivalence in symmetric algebras

对称代数中的反常等价

• 发表时间: 2018
• 作者: William Wong

Okuyama’s tilting complex and mutation

奥山的倾斜复合体和突变

• 发表时间: 2018
• 作者: Hon Yin Wong

Perverse equivalence

反常的等价

• 发表时间: 2018
• 作者: Willian Wong