Superconformal algebras and transitive group actions on quadrics (Q1360576)

The author gives a classification of so-called ``physical'' superconformal algebras. 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 superconformal algebra constructed by \textit{S.-T. Cheng} and \textit{V. G. Kac} [A new \(N=6\) superconformal algebra, Commun. Math. Phys. 186, No. 1, 219-231 (1997)]. The proof relies heavily on the classification of all the connected subgroups of \(SO_N(\mathbb{C})\) that act transitively on the quadric \((v,v)=1\).