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triple system

Proceedings of the Edinburgh Mathematical Society (1)

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CONSTRUCTION OF LIE SUPERALGEBRAS $D(2,1;\alpha)$,\$G(3)$ AND $F(4)$ FROM SOME TRIPLE SYSTEMS
Noriaki Kamiya, Susumu Okubo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 1 / February 2003

Published online by Cambridge University Press:

27 January 2003, pp. 87-98
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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