A construction of Lie algebras from a class of ternary algebras

Faulkner, John R.

doi:10.1090/S0002-9947-1971-0294424-X

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
DOI: https://doi.org/10.1090/S0002-9947-1971-0294424-X
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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