Classifying torsion classes for algebras with radical square zero via sign decomposition

To study the set of torsion classes a finite dimensional basic algebra over field, we use decomposition, called sign-decomposition, parameterized by elements {±1}n where n is number simple modules. If A an with radical square zero, then for each ϵ∈{±1}n there hereditary Aϵ! zero and bijection between associated to ϵ faithful Aϵ!. Furthermore, this preserves property being functorially finite. From point view tilting theory, it implies that isomorphism two-term silting complexes Aϵ!-modules. As application, prove Brauer line algebras (respectively, cycle algebras) having edges (2nn) 22n−1 if odd, ∞ even).