Gauging the d = 5 Maxwell/Einstein supergravity theories: More on Jordan algebras

We discuss in detail the possible gaugings, abelian and non-abelian, of a class of d = 5 Maxwell/Einstein supergravity theories for which the manifold of scalar fields is a symmetric coset space. We show that a U(1) "gauged" d =5 supergravity theory is possible with a vanishing scalar field potential, and we give necessary and sufficient conditions for this to occur. We discuss the d = 5 Yang-Mills/Einstein supergravity theories for both compact and non-compact gauge groups. We show that the "irreducibililty" of the "magical" subclass of d = 5 Maxwell/Einstein supergravity theories is preserved if and only if the Yang-Mills gauge group is SU(3,1). We expect that the irreducibility property of the "exceptional" d = 4 Maxwell/Einstein supergravity theory can similarly be preserved by gauging an SO^*(8) subgroup of its symmetry group E_7(-25). Throughout we make extensive use of the underlying Jordan algebraic structure of N = 2 supergravity which we have established in previous work.