  We address the construction of manifest U-duality invariant generalized
diffeomorphisms. The closure of the algebra requires an extension of the
tangent space to include a tensor hierarchy indicating the existence of an
underlying unifying structure, compatible with E_{11} and Borcherds algebras
constructions. We begin with four-dimensional gauged maximal supergravity, and
build a generalized Lie derivative that encodes all the gauge transformations
of the theory. A generalized frame is introduced, which accommodates for all
the degrees of freedom, including the tensor hierarchy. The generalized Lie
derivative defines generalized field-dependent fluxes containing all the
covariant quantities in the theory, and the closure conditions give rise to
their corresponding Bianchi Identities. We then move towards the construction
of a full generalized Lie derivative defined on an extended space, analyze the
closure conditions, and explore the connection with that of maximal gauged
supergravity via a generalized Scherk-Schwarz reduction, and with
11-dimensional supergravity.
