The local symmetries of M-theory and their formulation in generalised geometry

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In the doubled field theory approach to string theory, the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space. The local symmetries are then given by a generalised Lie derivative and its associated algebra. This paper constructs an analogous structure for M-theory. A crucial by-product of this is the derivation of the physical section condition for M-theory formulated in an extended space.