On the underlying E11 symmetry of the D=11 Free Differential Algebra

Abstract

We study the reduction of the Free Differential Algebra (FDA) of D=11 supergravity to an ordinary algebra. We show that in flat background and with vanishing three-form field strength, the corresponding minimal FDA can be reduced to an Inonu-Wigner contraction of Sezgin's M-Algebra. We also prove that in flat background but with a non trivial three-form field strength, the bosonic FDA can be reduced to the lowest levels of E11. This result suggests that the E11 symmetries, which act on perturbative states as well, are already encoded in the D=11 FDA and are made explicit when the theory is formulated on a enlarged group manifold.