  We present a construction which associates an infinite sequence of Kac-Moody
algebras, labeled by a positive integer n, to one single Jordan algebra. For
n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our
generalization utilizes a new relation between different generalized Jordan
triple systems, together with their known connections to Jordan and Lie
algebras. Applied to the Jordan algebra of hermitian 3x3 matrices over the
division algebras R, C, H, O, the construction gives the exceptional Lie
algebras f4, e6, e7, e8 for n=2. Moreover, we obtain their infinite-dimensional
extensions for n greater or equal to 3. In the case of 2x2 matrices the
resulting Lie algebras are of the form so(p+n,q+n) and the concomitant
nonlinear realization generalizes the conformal transformations in a spacetime
of signature (p,q).
