Extended Lie derivatives and a new formulation of D=11 supergravity

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Introducing an extended Lie derivative along the dual of A, the three-form field of d=11 supergravity, the full diffeomorphism algebra of d=11 supergravity is presented. This algebra suggests a new formulation of the theory, where the three-form field A is replaced by bivector Bab, bispinor Bαβ, and spinor-vector ηᵃβ one-forms. Only the bivector one-form Bab is propagating, and carries the same degrees of freedom of the three-form in the usual formulation, its curl [μ Babν] being related to the Fμνₐ b curl of the three-form. The other one-forms are auxiliary, and the transformation rules on all the fields close on the equations of motion of d=11 supergravity.