Superconformal algebras and transitive group actions on quadrics

A classification of ''physical'' superconformal algebras is given. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, the N = 2, 3 and 4 algebras, the superalgebra of all vector fields on the N = 2 supercircle, and a new algebra CK6 constructed in [3]. The proof relies heavily on the classification of all connected subgroups of SON(C) which act transitively on the quadric (v, v) = 1.