Tuesday, August 15, 14:00, 7.527

Yiping Chen (Wuhan University),
Singular equivalences and the Auslander-Reiten conjecture.

Abstract:

Let *k* be a field, and *A* be a finite dimensional *k*-algebra.
The Auslander-Reiten conjecture says that every finitely generated left
*A*-module *M* satisfying that
*Ext*^{n}_{A}(M, M ⊕ A)=0 for all
*n>0* must be projective.
The Auslander-Reiten conjecture is closely connected with the famous
Nakayama conjecture and the finitistic dimension conjecture.
In this talk, we will discuss this conjecture under certain singular
equivalences, and show that it holds for all skew-gentle algebras.