Generalised supersymmetry and p-brane actions

We investigate the most general N = 1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q, Q} similar to P is not special, and in fact must be treated democratically with a whole class of supersymmetries. We show that there are two distinct types of grading, and a new class of general spinors is defined. The associated superspaces are shown to be either of the usual type, or flat with no torsion, p-branes are discussed in these general superspaces and twelve dimensions emerges as maximal. New types of brane are discovered which could explain many features of the standard p-brane theories. (C) 1997 Elsevier Science B.V.