Seminario Dottorato 2024/25 - Enrico SABATINI (19.12.2024)

In the vast universe of representation theory there are two very separate and different worlds: commutative rings and finite dimensional (non-commutative) algebras. The problem of characterising certain subcategories, like many other problems, has been solved in both fields. However, the main techniques used for one context are generally not transferable to the other. Recently, some authors have focused their interest on a special kind of algebras that partially merge the two fields. Here, the apparently different results have a surprising generalisation and a unifying proof. 

In this talk, I will give an overview of the two fields mentioned above, describe their main features and give an idea of what allows such characterisations; avoiding all the technicalities. Finally, I'll show how the generalisation works with the aid of some interesting examples.