Maximal self-orthogonal modules and a new generalization of tilting modules
Seminar Talk in South Osaka Algebra Seminar at Zoom
Based on my preprint:
In this talk, we will introduce the study of self-orthogonal modules using projectively Wakamatsu tilting modules, which are a new generalization of tilting modules to possibly infinite projective dimensions defined by Ext-perpendicular categories. We will prove the equivalence of projectively Wakamatsu tilting, Wakamatsu tilting, maximal self-orthogonal, and full-rank self-orthogonal modules in the representation-finite case. Additionally, we will discuss some open conjectures related to self-orthogonal modules and their connections to homological conjectures.