Spinor Algebras and Extended Superconformal Algebras

Abstract

We consider supersymmetry algebras in arbitrary spacetime dimension and signature. Minimal and maximal superalgebras are given for single and extended supersymmetry. It is seen that the supersymmetric extensions are uniquely determined by the properties of the spinor representation, which depend on the dimension $D$ mod 8 and the signature $|ρ|$ mod 8 of spacetime.