CONICET | Buscador de Institutos y Recursos Humanos

We address the construction of manifest U-duality invariant generalized dif- feomorphisms. 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, com- patible with E11 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 accommo- dates 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 Identi- ties. 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.