The superconformal algebra in higher dimensions

The superconformal algebra for 4/4N-dimensional super-Minkowski space (d=4) can be identified with the simple superalgebra su (2,2/N). For even-dimension d=5,6 the superconformal algebra can be identified with a real form of the simple superalgebras F(4), D(4,1) respectively in Kac's classification. For even-dimension d>-7 it is impossible to define a superconformal algebra satisfying three natural conditions: (1) it acts as infinitesimal automorphisms on super-Minkowski space; (2) this action extends the natural action of the super-Poincaré algebra; (3) when the action of the even part of the superconformal algebra is reduced to an infinitesimal action on ordinary Minkowski space, it extends the natural action of the conformal algebra so (2, d).