Memoirs of the American Mathematical Society 2001; 140 pp; softcover Volume: 150 ISBN10: 082182645X ISBN13: 9780821826454 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/150/711
 We classify graded simple Jordan superalgebras of growth one which correspond the so called "superconformal algebras" via the TitsKantorKoecher construction. The superconformal algebras with a "hidden" Jordan structure are those of type \(K\) and the recently discovered ChengKac 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. Readership Graduate students and research mathematicians interested in nonassociative rings and algebras. Table of Contents  Introduction
 Structure of the even part
 Cartan type
 Even part is direct sum of two loop algebras
 \(A\) is a loop algebra
 \(J\) is a finite dimensional Jordan superalgebra or a Jordan superalgebra of a superform
 The main case
 Impossible cases
 Bibliography
