Classification of exact structures and CM-finite Gorenstein algebras


Seminar Talk in Ring Theory and Representation Theory Seminar at Nagoya University, Japan

Based on paper:


In this talk, I will give a classification of all possible exact structures on a given additive category, in terms of the module category over it. For a category of finite type, an exact structure corresponds to a set of dotted arrows of the AR quiver of it, or a set of simple modules satisfying the 2-regular condition. Using this, we reduce a classification of CM-finite Iwanaga-Gorenstein algebras to that of algebras with finite global dimension, which enables us to construct such algebras explicitly.