报告题目：Homological Theory of Orthogonal Modules

报告时间：2023-01-04  15:00 - 16:00

报告人：陈红星 教授  首都师范大学

腾讯会议ID：308 410 239

报告链接：https://meeting.tencent.com/dm/HQv7lxyUZnAz

Abstract：Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important part of the Nakayama conjecture. In this talk, we discuss finitely generated, orthogonal generators over a self-injective Artin algebra from the view point of stable module categories. As a result, for an orthogonal generator, we establish a recollement of its relative stable categories, describe compact objects of the right term of the recollement, and give equivalent characterizations of Tachikawa's second conjecture in terms of relative Gorenstein categories. Further, we introduce Gorenstein-Morita algebras and show that the Nakayama conjecture holds true for them. This is joint work with Changchang Xi.