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CONSTRUCTION OF LIE SUPERALGEBRAS $D(2,1;\alpha)$,\$G(3)$ AND $F(4)$ FROM SOME TRIPLE SYSTEMS

Published online by Cambridge University Press:  27 January 2003

Noriaki Kamiya  and
Susumu Okubo
Noriaki Kamiya
Affiliation:
Department of Mathematics, The University of Aizu, Tsuruga, Aizu-Wakamatsu City, Fukushima, Japan (kamiya@u-aizu.ac.jp)
Susumu Okubo
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA (okubo@pas.rochester.edu)
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Abstract

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We have constructed Lie superalgebras $D(2,1;\alpha)$, $G(3)$ and $F(4)$ from $U(-1,-1)$-balanced Freudenthal–Kantor triple systems in a natural way.

AMS 2000 Mathematics subject classification: Primary 17A40; 17B60

Keywords

Lie superalgebrastriple systemoctonions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 87 - 98
Copyright
Copyright © Edinburgh Mathematical Society 2003