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，我们研究了一种对应于两项倾斜的反常等价。一般来说，并不是所有的两个任期的倾斜都是反常的对等。具有全部二项倾斜复形的代数的条件可以用Jasso约化来描述。此外，还对预射影代数的特殊情况进行了研究。其中我们确定了两项倾斜的倒等价类型，并将其与对称群的组合学联系起来。我们还建立了Rouquier-Okuyama倾斜复形与倒等价之间的联系，正如项目开始时所建议的那样。除了以上的主要进展外，我们与名古屋大学的Aaron Chan共同完成了一些对称群表示的p-复形的同调工作。与TUS的工作进行得令人满意。

项目成果

Derived Equivalence and Perverse Equivalence

派生等价和反常等价

• 发表时间: 2019
• 作者: B. Gonzalez-Izquierdo;T. A. Pikuz;A. Sagisaka;Z. E. Davidson;K. Ogura;A. Bierwage;K. Huang;T. Zh. Esirkepov;J. K. Koga;A. Ya. Lopatin;Y. Fukuda;M. Ishino;E. N. Ragozin;S. A. Pikuz;N. I. Chkhalo;N. N. Salashchenko;D. Neely;P. McKenna;H. K;Hon Yin Wong
• 通讯作者: 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: Toni M. Maier;Yasuhiro Ikabata;Hiromi Nakai;William Wong
• 通讯作者: William Wong

Homological Approach to Representations

表示的同调方法

• 发表时间: 2018
• 作者: B. Gonzalez-Izquierdo;T. A. Pikuz;A. Sagisaka;Z. E. Davidson;K. Ogura;A. Bierwage;K. Huang;T. Zh. Esirkepov;J. K. Koga;A. Ya. Lopatin;Y. Fukuda;M. Ishino;E. N. Ragozin;S. A. Pikuz;N. I. Chkhalo;N. N. Salashchenko;D. Neely;P. McKenna;H. K;Hon Yin Wong;Hon Yin Wong
• 通讯作者: Hon Yin 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: B. Gonzalez-Izquierdo;T. A. Pikuz;A. Sagisaka;Z. E. Davidson;K. Ogura;A. Bierwage;K. Huang;T. Zh. Esirkepov;J. K. Koga;A. Ya. Lopatin;Y. Fukuda;M. Ishino;E. N. Ragozin;S. A. Pikuz;N. I. Chkhalo;N. N. Salashchenko;D. Neely;P. McKenna;H. K;Hon Yin Wong;Hon Yin Wong;Hon Yin Wong
• 通讯作者: Hon Yin Wong

Perverse equivalence

反常的等价

• 发表时间: 2018
• 作者: Calum McDonald;Chengsheng Ni;Paul Maguire;Davide Mariotti and Vladimir Svrcek;Willian Wong
• 通讯作者: Willian Wong