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Graded Simple Jordan Superalgebras of Growth One
V. G. Kac, Massachusetts Institute of Technology, Cambridge, MA, C. Martinez, Universidad de Oviedo, Spain, and E. Zelmanov, Yale University, New Haven, CT

Memoirs of the American Mathematical Society
2001; 140 pp; softcover
Volume: 150
ISBN-10: 0-8218-2645-X
ISBN-13: 978-0-8218-2645-4
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/150/711
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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.


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
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