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We address the construction of manifest U-duality invariant generalizeddiffeomorphisms. The closure of the algebra requires an extension of thetangent space to include a tensor hierarchy indicating the existence of anunderlying unifying structure, compatible with E_{11} and Borcherds algebrasconstructions. We begin with four-dimensional gauged maximal supergravity, andbuild a generalized Lie derivative that encodes all the gauge transformationsof the theory. A generalized frame is introduced, which accommodates for allthe degrees of freedom, including the tensor hierarchy. The generalized Liederivative defines generalized field-dependent fluxes containing all thecovariant quantities in the theory, and the closure conditions give rise totheir corresponding Bianchi Identities. We then move towards the constructionof a full generalized Lie derivative defined on an extended space, analyze theclosure conditions, and explore the connection with that of maximal gaugedsupergravity via a generalized Scherk-Schwarz reduction, and with11-dimensional supergravity.

The gauge structure of Exceptional Field Theories and the tensor hierarchy