Bricks and mutation

Abstract

We investigate the lattice of torsion pairs in the category of modules over an Artinian ring via the corresponding HRS-tilted t-structures. Through this lens, we give a unified account of two known results about the Hasse diagram of the lattice: that the edges of the diagram have a canonical labelling by bricks [Barnard, Carroll, and Zhu (2019); Demonet, Iyama, Reading, Reiten, and Thomas (2023)] and that the edges correspond to irreducible mutations of maximal rigid sets in the derived category [Angeleri Hügel, Laking, Šťovíček, and Vitória (2022)].