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 | References | Similar Articles | Additional Information
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
Keywords:
Lie algebras,
Jordan algebras,
ternary algebra,
simple Lie algebras,
Lie algebras of type <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${E_7}$">,
Lie algebras of type <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img6.gif" ALT="${E_8}$">
Article copyright:
© Copyright 1971
American Mathematical Society