The answer is falciform ligament. It also separates the left lobe into lateral and medial segments. It is a type of peritoneum (composed of two layers of tightly bound peritoneums). The ligament stretches from the underside of the diaphragm to the posterior surface of the sheath of the right rectus abdominis muscle, as low down as the umbilicus; by its right margin, it extends from the notch on the anterior margin of the liver, as far back as the posterior surface.