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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new construction of the Kac Jordan superalgebra
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by Georgia Benkart and Alberto Elduque PDF
Proc. Amer. Math. Soc. 130 (2002), 3209-3217 Request permission

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
  • 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, DOI 10.1006/jabr.1999.7877
  • Leo F. Epstein, A function related to the series for $e^{e^x}$, J. Math. Phys. Mass. Inst. Tech. 18 (1939), 153–173. MR 58, DOI 10.1002/sapm1939181153
  • V. G. Kac, Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), no. 13, 1375–1400. MR 498755, DOI 10.1080/00927877708822224
  • I. Kaplansky, Graded Jordan Algebras I, preprint.
  • Kevin McCrimmon, Kaplansky superalgebras, J. Algebra 164 (1994), no. 3, 656–694. MR 1272110, DOI 10.1006/jabr.1994.1085
  • C. MartĂ­nez and E. Zelmanov, Simple finite dimensional Jordan superalgebras of prime characteristic, J. Algebra 236 (2001), 575–629.
  • M. Racine and E. Zelmanov, Classification of simple Jordan superalgebras with semisimple even part, to appear.
  • I.P. Shestakov, Lecture, Jordan Algebren Conference, Oberwolfach, Germany, 1996.
  • I.P. Shestakov, private communication, June 2001.
  • A. S. Shtern, Representations of an exceptional Jordan superalgebra, Funktsional. Anal. i Prilozhen. 21 (1987), no. 3, 93–94 (Russian). MR 911787
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Additional Information
  • Georgia Benkart
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 34650
  • Email: benkart@math.wisc.edu
  • Alberto Elduque
  • Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
  • MR Author ID: 208418
  • Email: elduque@posta.unizar.es
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 3209-3217
  • MSC (2000): Primary 17A70, 17B60
  • DOI: https://doi.org/10.1090/S0002-9939-02-06466-3
  • MathSciNet review: 1912998