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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A construction of Lie algebras from a class of ternary algebras


Author: John R. Faulkner
Journal: Trans. Amer. Math. Soc. 155 (1971), 397-408
MSC: Primary 17B05
MathSciNet review: 0294424
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Abstract: A class of algebras with a ternary composition and alternating bilinear form is defined. The construction of a Lie algebra from a member of this class is given, and the Lie algebra is shown to be simple if the form is nondegenerate. A characterization of the Lie algebras so constructed in terms of their structure as modules for the three-dimensional simple Lie algebra is obtained in the case the base ring contains 1/2. Finally, some of the Lie algebras are identified; in particular, Lie algebras of type $ {E_8}$ are obtained.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0294424-X
PII: S 0002-9947(1971)0294424-X
Keywords: Lie algebras, Jordan algebras, ternary algebra, simple Lie algebras, Lie algebras of type $ {E_7}$, Lie algebras of type $ {E_8}$
Article copyright: © Copyright 1971 American Mathematical Society