科学研究
报告题目:

SinguIar equivaIences and the AusIander-Reiten conjecture

报告人:

陈一萍 副教授(金沙9001cc诚为本)

报告时间:

报告地点:

数学院二楼报告厅

报告摘要:

Let $k$ be a field, and $A$ be a finite dimensional $k$-algebra. The Auslander-Reiten conjecture (or generalized Nakayama conjecture) says that every finitely generated left $A$-module $M$ satisfying that $\Ext^i_A(M, M\oplus A)=0$ for all $i>0$ must be projective.

The Auslander-Reiten conjecture is still open now, and plays a central role in the representation theory of algebras. And it is closely connected with the celebrated Nakayama conjecture and the finitistic dimension conjecture.

In this talk, we will discuss the behaviors of this conjecture under certain singular equivalences induced by adjoint pairs (joint work with Wei Hu, Yongyun Qin and Ren Wang). As an application, we prove that this conjecture holds for all skew-gentle algebras.