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We present the supersymmetric completion of the M-theory free differentialalgebra resulting from a compactification to four dimensions on a twistedseven-torus with 4-form and 7-form fluxes turned on. The super--curvatures aregiven and the local supersymmetry transformations derived. Dual formulations ofthe theory are discussed in connection with classes of gaugings correspondingto diverse choices of vacua. This also includes seven dimensionalcompactifications on more general spaces not described by group manifolds.Comment: 19 pages, LaTeX, typos corrected, references adde

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes