  We discuss the structure of 4D gauged supergravity algebras corresponding to
globally non-geometric compactifications of F-theory, admitting a local
geometric description in terms of 10D supergravity. By starting with the well
known algebra of gauge generators associated to non-geometric type IIB fluxes,
we derive a full algebra containing all, closed RR and NSNS, geometric and
non-geometric dual fluxes. We achieve this generalization by a systematic
application of SL(2,Z) duality transformations and by taking care of the
spinorial structure of the fluxes. The resulting algebra encodes much
information about the higher dimensional theory. In particular, tadpole
equations and Bianchi identities are obtainable as Jacobi identities of the
algebra. When a sector of magnetized (p,q) 7-branes is included, certain closed
axions are gauged by the U(1) transformations on the branes. We indicate how
the diagonal gauge generators of the branes can be incorporated into the full
algebra, and show that Freed-Witten constraints and tadpole cancellation
conditions for (p,q) 7-branes can be described as Jacobi identities satisfied
by the algebra mixing bulk and brane gauge generators.
