  It is known that black hole charge vectors of N=8 and magic N=2 supergravity
in four and five dimensions can be represented as elements of Jordan algebras
of degree three over the octonions and split-octonions and their Freudenthal
triple systems. We show both such Jordan algebras are contained in the
exceptional Jordan C*-algebra and construct its corresponding Freudenthal
triple system and single variable extension. The transformation groups for
these structures give rise to the complex forms of the U-duality groups for N=8
and magic N=2 supergravities in three, four and five dimensions.
