Friday, August 3, 14:00, 7.527
Osamu Iyama (Nagoya), τ-tilting theory.

Abstract:
We introduce τ-rigid modules and (support) τ-tilting modules as generalizations of partial tilting modules and tilting modules. These notions appear in work of Auslander-Smalo in 1981 without names. We show that they improve tilting theory from the viewpoint of mutation, i.e. any indecomposable summand of a support τ-tilting module can be replaced in a unique way to get a new support τ-tilting module. Moreover, when the algebra is 2-Calabi-Yau tilted, we have a natural bijection between support τ-tilting modules and cluster tilting objects.