A characterization of hereditary algebras via thick subcategories

Let Λ \Lambda be a finite dimensional algebra. There exists a natural injective map from the set of wide subcategories in the category of finitely generated Λ \Lambda -modules to the set of thick subcategories in the bounded derived category of Λ \Lambda .We show, when Λ \Lambda is elementary, that the natural map is bijective if and only if Λ \Lambda is hereditary.