E₇₍₇₎ symmetry and dual gauge algebra of M-theory on a twisted seven-torus

We consider M-theory compactified on a twisted 7-torus with fluxes when all the seven antisymmetric tensor fields in four dimensions have been dualized into scalars and thus the E_{7(7)} symmetry is recovered. We find that the Scherk--Schwarz and flux gaugings define a ``dual'' gauge algebra, subalgbra of E_{7(7)}, where some of the generators are associated with vector fields which are dual to part of the original vector fields (deriving from the 3-form). In particular they are dual to those vector fields which have been ``eaten'' by the antisymmetric tensors in the original theory by the (anti-)Higgs mechanism. The dual gauge algebra coincides with the original gauge structure when the quotient with respect to these dual (broken) gauge generators is taken. The particular example of the S-S twist corresponding to a ``flat group'' is considered.