On algebras satisfying
$x^2x^2=N(x)x$ |
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Authors: | Alberto Elduque Susumu Okubo |
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Institution: | (1) Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain, ES;(2) Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA, US |
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Abstract: | The commutative algebras satisfying the “adjoint identity”:
, where N is a cubic form, are shown to be related to a class of generically algebraic Jordan algebras of degree at most 4 and to the
pseudo-composition algebras. They are classified under a nondegeneracy condition.
As byproducts, the associativity of the norm of any pseudo-composition algebra is proven and the unital commutative and power-associative
algebras of degree are shown to be Jordan algebras.
Received January 26, 1999; in final form August 26, 1999 / Published online July 3, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 17C50 17A30 |
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