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

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 B^{ab}, bispinor B^{\alpha\beta}, and spinor-vector \eta^{a\beta} one-forms. Only the bivector one-form B^{ab} is propagating, and carries the same degrees of freedom of the three-form in the usual formulation, its curl \Dcal_{[\mu} B^{ab}_{\nu]} being related to the F_{\mu \nu a 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.