Symmetric subcategories, tilting modules and derived recollements

：陈红星（首都师范大学）
：2022-11-18 15:00
：腾讯会议 ID：342-853-386（无密码）

报告人：陈红星（首都师范大学）

时  间：11月18日下午15:00

地  点：腾讯会议 ID：342-853-386（无密码）

内容摘要:

In the general context of tilting theory, a central theme is to study relations between the derived module categories of the given algebras and the endomorphism algebras of tilting modules. In the talk, we introduce symmetric subcategories and show that for any good tilting module T over an algebra A, the derived category of the endomorphism algebra B of T is a recollement of the derived categories of A and a symmetric subcategory of the module category of B, in the sense of Beilinson-Bernstein-Deligne. Thus the kernel of the total left-derived tensor functor induced by a good tilting module is always triangle equivalent to the derived category of a symmetric subcategory of a module category. Explicit description of symmetric subcategories associated to a class of good 2-tilting modules over commutative Gorenstein local rings are presented. This is joint work with Changchang Xi.

个人简介：

陈红星，首都师范大学数学科学学院教授，德国洪堡访问学者，博士毕业于北京师范大学。研究方向为代数表示论与同调代数，主要从事经典同调猜想、导出范畴、倾斜与粘合理论等方面的研究。2021年获国家自然科学基金优秀青年科学基金。研究成果发表在Proc. Lond. Math. Soc、Trans. Amer. Math. Soc、Int Math Res Notices等国际数学杂志上。

 

联系人：王清