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Transactions of the American Mathematical Society

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

 

 

Lie-admissible, nodal, noncommutative Jordan algebras


Author: D. R. Scribner
Journal: Trans. Amer. Math. Soc. 154 (1971), 105-111
MSC: Primary 17A15
MathSciNet review: 0314919
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Abstract: The main theorem is that if A is a central simple flexible algebra, with an identity, of arbitrary dimension over a field F of characteristic not 2, and if A is Lie-admissible and $ {A^ + }$ is associative, then $ {\text{ad}}\;(A)' = [A,A]/F$ is a simple Lie algebra. It is shown that this theorem applies to simple nodal noncommutative Jordan algebras of arbitrary dimension, and hence that such an algebra A also has derived algebra $ {\text{ad}}\;(A)'$ simple.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0314919-X
Keywords: Nodal algebras, noncommutative Jordan algebras, Lie-admissible algebras, infinite-dimensional algebras
Article copyright: © Copyright 1971 American Mathematical Society