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Proceedings of the American Mathematical Society
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
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-02-06466-3
PII: S 0002-9939(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