Tilting up algebras of small homological dimensions

We consider algebras Λ which satisfy the property that for each indecomposable module ΛX, either its projective dimension pd ΛX is at most one or its injective dimension id ΛX is at most one and that the global dimension gldim Λ is three. We will show that this class is in bijective correspondence with a class of algebras of global dimension two admitting a special tilting torsion pair.