On algebras satisfying x^2x^2=N(x)x

The commutative algebras satisfying the "adjoint identity" 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 3 are shown to be Jordan algebras.

(This paper has appeared in Math. Z. 235 (2000), 275 - 314)

A. Elduque <elduque@posta.unizar.es >