  Freudenthal triple systems come in two flavors, degenerate and nondegenerate.
The best criterion for distinguishing between the two which is available in the
literature is by descent. We provide an identity which is satisfied only by
nondegenerate triple systems. We then use this to define algebraic structures
whose automorphism groups produce all adjoint algebraic groups of type E_7 over
an arbitrary field of characteristic not 2 or 3.
  The main advantage of these new structures is that they incorporate a
previously unconsidered invariant (a symplectic involution) of these groups in
a fundamental way. As an application, we give a construction of adjoint groups
with Tits algebras of index 2 which provides a complete description of this
involution and apply this to groups of type E_7 over a real-closed field.
