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Third power associative composition algebras

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Abstract

Classical composition algebras, with a unit element, are well-known and can be obtained by means of the Cayley-Dickson doubling process. If the condition on the existence of unit element is dropped, many new algebras arise. However, it is shown in this paper that if such a weak condition as the associativity of third powers of any element is imposed, only the known flexible composition algebras appear.

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Authors and Affiliations

  1. Departmento de Matemáticas, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Alberto Elduque & José María Pérez

Authors
  1. Alberto Elduque
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  2. José María Pérez
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Additional information

Partially supported by the DGICYT (PS 90-0129) and by the DGA (PCB-6/91)

Supported by a grant from the ‘Plan de Formación del Personal Investigador’ (DGICYT, Spain)

This article was processed by the authors using the Springer-Verlag TEX P Jour1g macro package 1991.

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Elduque, A., Pérez, J.M. Third power associative composition algebras. Manuscripta Math 84, 73–87 (1994). https://doi.org/10.1007/BF02567444

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