Classifications of exact structures and CM-finite Iwanaga-Gorenstein algebras


Conference Talk in International Conference on Representations of Algebras (ICRA 2018) at Czech Technical University in Prague, Czech Republic

Based on paper:


In this talk, we consider Quillen’s exact categories and their applications to representation theory. We 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 with finitely many indecomposables, 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.