Supersymmetry, p-brane duality, and hidden spacetime dimensions

A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions ina theory that treats p-branes democratically. The maximal number of dimensions is 12, with signature (10,2), containing one space and one time dimension that are hidden from the point of view of perturbative ten-dimensional string theory or its compactifications. When the theory is compactified on R(d-1,1) x T-c+1,T-1 with d + c + 2 = 12, there are isometry groups that relate to the hidden dimensions as well as to duality. Their combined intersecting classification schemes provide some properties of nonperturbative states and their couplings.