SUPERCONFORMAL ALGEBRAS AND CLIFFORD ALGEBRAS

It is shown that superconformal Lie superalgebras contain a Clifford algebra structure. This is used to present a classification of these algebras under the following assumptions: only fields with (half-)integer conformai dimension between 2 and 1/2, and a nonzero central element. It turns out that the number of super-symmetry generators must be less than or equal to 4. More generally, the so (N) series, as well as some nonassociative algebras connected to S7, also have a natural place in this Clifford algebra framework. © 1990 American Institute of Physics.