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A new construction of the Kac Jordan superalgebra

Author(s): Georgia Benkart; Alberto Elduque
Journal: Proc. Amer. Math. Soc. 130 (2002), 3209-3217.
MSC (2000): Primary 17A70, 17B60
Posted: April 17, 2002
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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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V.G. Kac, Classification of $\mathbb Z$-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), 1375-1400. MR 58:16806

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C. Martínez and E. Zelmanov, Simple finite dimensional Jordan superalgebras of prime characteristic, J. Algebra 236 (2001), 575-629. CMP 2001:08

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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: 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
Posted: 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 Cient{í}fica (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 of article: Copyright 2002, American Mathematical Society

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