Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A new construction of the Kac Jordan superalgebra


Authors: Georgia Benkart and Alberto Elduque
Journal: Proc. Amer. Math. Soc. 130 (2002), 3209-3217
MSC (2000): Primary 17A70, 17B60
Published electronically: April 17, 2002
MathSciNet review: 1912998
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an elementary construction of the 10-dimensional simple Jordan superalgebra K$_{10}$ of Kac using the 3-dimensional tiny Kaplansky superalgebra. This new realization of K$_{10}$ enables us to derive many of its properties.


References [Enhancements On Off] (What's this?)

  • [BDE] Pilar Benito, Cristina Draper, and Alberto Elduque, On some algebras related to simple Lie triple systems, J. Algebra 219 (1999), no. 1, 234–254. MR 1707670, 10.1006/jabr.1999.7877
  • [HK] V. G. Kac, Classification of simple 𝑍-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), no. 13, 1375–1400. MR 0498755
    Leslie Hogben and Victor G. Kac, Erratum: “Classification of simple 𝑍-graded Lie superalgebras and simple Jordan superalgebras” [Comm. Algebra 5 (1977), no. 13, 1375–1400; MR0498755 (58 #16806)] by Kac, Comm. Algebra 11 (1983), no. 10, 1155–1156. MR 700729
  • [K] V. G. Kac, Classification of simple 𝑍-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), no. 13, 1375–1400. MR 0498755
  • [Kp] I. Kaplansky, Graded Jordan Algebras I, preprint.
  • [M] Kevin McCrimmon, Kaplansky superalgebras, J. Algebra 164 (1994), no. 3, 656–694. MR 1272110, 10.1006/jabr.1994.1085
  • [MZ] C. Martínez and E. Zelmanov, Simple finite dimensional Jordan superalgebras of prime characteristic, J. Algebra 236 (2001), 575-629. CMP 2001:08
  • [RZ] M. Racine and E. Zelmanov, Classification of simple Jordan superalgebras with semisimple even part, to appear.
  • [S1] I.P. Shestakov, Lecture, Jordan Algebren Conference, Oberwolfach, Germany, 1996.
  • [S2] I.P. Shestakov, private communication, June 2001.
  • [Sh] A. S. Shtern, Representations of an exceptional Jordan superalgebra, Funktsional. Anal. i Prilozhen. 21 (1987), no. 3, 93–94 (Russian). MR 911787

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 17A70, 17B60

Retrieve articles in all journals with MSC (2000): 17A70, 17B60


Additional Information

Georgia Benkart
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: benkart@math.wisc.edu

Alberto Elduque
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: elduque@posta.unizar.es

DOI: https://doi.org/10.1090/S0002-9939-02-06466-3
Keywords: Kac superalgebra, Kaplansky superalgebra
Received by editor(s): June 25, 2001
Published electronically: April 17, 2002
Additional Notes: The first author gratefully acknowledges support from National Science Foundation Grant #DMS–9970119
The second author has been supported by the Spanish DGES (Pb 97-1291-C03-03) and by a grant from the Spanish Dirección General de Enseñanza Superior e Investigación Científica (Programa de Estancias de Investigadores Españoles en Centros de Investigación Extranjeros), while visiting the University of Wisconsin at Madison.
Dedicated: To Irving Kaplansky
Communicated by: Lance W. Small
Article copyright: © Copyright 2002 American Mathematical Society