  We introduce the notion of a generalized representation of a Jordan algebra
with unit. The greneralized representation has the following properties:
  (1) Usual representations and Jacobson representations correspond to special
cases of generalized representations.
  (2) Every simple Jordan algebra has infinitely many nonequivalent generalized
representations.
  (3) There is a one-to-one correspondence between irreducible generalized
representations of a Jordan algebra A and irreducible representations of a
graded Lie algebra L(A)=U_{-1}\oplus U_0\oplus U_1 corresponding to A (the Lie
algebra L(A) coincides with the TKK construction when A has a unit).
  The latter correspondence allows to use the theory of representations of Lie
algebras to study generalized representations of Jordan algebras. In
particular, one can classify irreducible generalized representations of
semisimple Jordan algebras and also obtain classical results about usual
representations and Jacobson representations in a simple way.
