Graded Simple Jordan Superalgebras of Growth One

by Victor G. Kac, Efim Zelmanov, Celso Martínez Carracedo

We classify graded simple Jordan superalgebras of growth one which correspond the so called 'superconformal algebras' via the Tits-Kantor-Koecher construction. The superconformal algebras with a 'hidden' Jordan structure are those of type $K$ and the recently discovered Cheng-Kac superalgebras $CK(6)$. We show that Jordan superalgebras related to the type $K$ are Kantor Doubles of some Jordan brackets on associative commutative superalgebras and list these brackets.

140 pages, Paperback

First published March 1, 2001