An introduction to the lattice of torsion classes

TL;DR

This paper introduces the structure of the lattice of torsion classes in finite-dimensional algebras, highlighting its complete semidistributivity and connecting it to recent research developments.

Contribution

It provides an accessible overview of the lattice of torsion classes, emphasizing its key properties and recent advances in the field.

Findings

Lattice of torsion classes is completely semidistributive.

Highlights connections to recent research by Barnard-Carroll-Zhu and Demonet-Iyama-Reading-Reiten-Thomas.

Serves as an introductory exposition to the topic.

Abstract

In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as an introduction to recent work by Barnard-Carroll-Zhu and Demonet-Iyama-Reading-Reiten-Thomas.