A rational construction of Lie algebras of type E7

We give an explicit construction of Lie algebras of type E7 out of a Lie algebra of type D6 with some restrictions. Up to odd degree extensions, every Lie algebra of type E7 arises this way. For Lie algebras that admit a 56-dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations.