  Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative
non-associative algebras.
  In previous work, we gave an explicit description of these algebras for
groups of type $G_2,F_4$ and certain forms of $E_6$ in terms of octonion and
Albert algebras. In this paper, we extend this further by dealing with $E_7$ in
terms of generalised Freudenthal triple systems.
