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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Lie algebras of type $ BC\sb{1}$


Author: B. N. Allison
Journal: Trans. Amer. Math. Soc. 224 (1976), 75-86
MSC: Primary 17B20
MathSciNet review: 0432724
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Abstract: Let L be a central simple Lie algebra of type $ B{C_1}$ with highest root space of dimension greater than one over a field of characteristic zero. It is shown that either L is isomorphic to the simple Lie algebra associated with a skew hermitian form of index one or L can be constructed from the tensor product of two composition algebras. This result is obtained by completing the description (begun in [3]) of the corresponding class of ternary algebras.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0432724-5
Keywords: Lie algebras, ternary algebras, Jordan algebras, Malcev algebras, simple Lie algebras, Lie algebras of type $ B{C_1}$
Article copyright: © Copyright 1976 American Mathematical Society