2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231053It is well-known that every algebraic group of type F_4 is the automorphism group of an exceptional Jordan algebra, and that up to isogeny all groups of type ^1E_6 with trivial Tits algebras arise as the isometry groups of norm forms of such Jordan algebras. We describe a similar relationship between groups of type E_6 and groups of type E_7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type E_7 with trivial Tits algebras. The underlying algebraic structure for the relationship considered here are a sort of 56-dimensional structurable algebra which are forms of an algebra constructed from an exceptional Jordan algebra.35 pages, AMSLaTeX -- error in final section correctedRings and AlgebrasAlgebraic Geometry17A30 (Primary) 11E72, 14L30, 17A40, 17B25, 17C30, 20G15 (Secondary)text