Foliations in supergravity

Following upon a previous paper [1] on the existence of chiral transformati ons in a foliated version of the Cremmer, Julia and Scherk model, we deduce a couple of interesting properties of the model. These are: (i) TM4 is isomorphic to a quotient Lie pseudoalgebra on the algebra of bas ic functions in M-11; (ii) There is a locally trivial fibration which exhibits M-11 as M-7 x U, U subset of W and W is the basic manifold of the foliation [5]; (iii) The chiral group of the model is identified as Cl-x(L, g(L)) x Cl-x(Q , g(Q)), the factors are respectively the multiplication groups of units in the Clifford algebras Cl-x(L, g(L)) and Cl-x(Q, g(Q)) and matching of this group with phenomenology is briefly discussed.