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An octonionic construction of the Kac superalgebra K$ _{10}$


Authors: M. L. Racine and E. I. Zel’manov
Journal: Proc. Amer. Math. Soc. 143 (2015), 1075-1083
MSC (2010): Primary 17C70, 17C40; Secondary 17A75, 17D05
DOI: https://doi.org/10.1090/S0002-9939-2014-12327-6
Published electronically: November 3, 2014
MathSciNet review: 3293723
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Abstract: The split Kac Jordan superalgebra K$ _{10}$, as well as its forms, are embedded in $ {\mathcal {M}}_2({\mathcal {O}})$, the 2 by 2 matrices with entries in the split octonion algebra $ \mathcal {O}$.


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Additional Information

M. L. Racine
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada
Email: mracine@uottawa.ca

E. I. Zel’manov
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112 — and — KAU, Jeddah, Saudi Arabia
Email: ezelmanov@ucsd.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12327-6
Keywords: Kac Jordan superalgebra, octonion
Received by editor(s): May 14, 2012
Received by editor(s) in revised form: July 23, 2013
Published electronically: November 3, 2014
Additional Notes: The first author is grateful to the Korea Institute for Advanced Study for its hospitality while part of this research was carried out.
The second author was supported in part by grants from NSF, DMS-0500568
Dedicated: Dedicated to Kevin McCrimmon on his seventieth birthday
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.