Ring Theory Seminar
Speaker: Lidia Angeleri Hügel (Università di Verona)
Title: The lattice of torsion pairs of a finite dimensional algebra
Date: 26/11/2025
Time: 10:00
Web: http://mat.uab.cat/web/ligat/
Abstract: The notion of a torsion pair is a tool widely employed in algebra, geometry, and topology. It provides a decomposition of an abelian category into smaller parts that are still big enough to reconstruct the whole category. Over a finite dimensional algebra A, the torsion pairs in the category mod(A) of finite dimensional modules form a complete lattice tors(A). It is an important invariant of A which encodes relevant information on the category of A-modules and its derived category D(A). In my talk, I will discuss the connection of tors(A) with another important invariant, the Ziegler spectrum Zg(D(A)) of D(A). This is a topological space originating from the model theory of modules that describes the theory of purity of D(A). We will see that certain distinguished intervals in tors(A) correspond to closed sets in Zg(D(A)), and we will describe the arrows in the Hasse quiver of tors(A) in terms of an operation of mutation. If time permits, I will also present an application to the theory of stability. This is a report on joint work with Rosanna Laking, Calvin Pfeifer, and Francesco Sentieri.