Torsion classes, wide subcategories and maximal green sequences

Abstract

In this thesis, the relationship between torsion classes and wide subcategories in module categories of finite dimensional algebras is studied. Of particular interest are wide intervals, which are interval subsets of the lattice of torsion classes that enclose a wide subcategory in a certain way. For a fixed wide subcategory, the set of wide intervals is described and new results relating this set with the lattice of torsion classes of some other finite dimensional algebra are obtained. In the second half, we study maximal green sequences for finite dimensional algebras. The well-known relationship to torsion classes allows us to integrate the terminology of wide intervals. Among several smaller results, we put this theory to use to prove a purely representation theoretic version of the Target before Source conjecture for quivers with potential.