Raqel Cohelo Simoes (Lancaster University) – Simple-mindedness

Abstract:

Module categories have two types of generators: projective modules and simple modules. Abstractions of projective modules have led to (tau-)tilting theory and cluster-tilting theory. Cluster-tilting theory is well suited to positive Calabi-Yau categories. However, there are natural examples of negative Calabi-Yau categories, such as the stable module category of a symmetric algebra. Projective generators are less useful in this context because they are killed by stabilisation, making understanding the simple-like generators an important question. 

In this talk I will explain how simple-minded systems are negative Calabi-Yau analogues of cluster-tilting objects and give an overview of aspects of their theory for hereditary algebras.