Advances in Applied Clifford Algebras

, Volume 27, Issue 2, pp 955–964 | Cite as

A Note on Standard Composition Algebras of Types II and III

  • P. D. Beites
  • A. P. Nicolás


Some identities satisfied by certain standard composition algebras, of types II and III, are studied and become candidates for the characterization of the mentioned types. Composition algebras of arbitrary dimension, over a field F with char\({(F) \neq 2}\) and satisfying the identity \({x^{2}y = n(x)y}\) are shown to be standard composition algebras of type II. As a consequence, the identity \({yx^{2} = n(x)y}\) characterizes the type III.

Mathematics Subject Classification

17A75 15A21 


Standard composition algebra Identity 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Departamento de Matemática, Centro de Matemática e Aplicações (CMA-UBI)Universidade da Beira InteriorCovilhãPortugal
  2. 2.Departamento de Matemática Aplicada, Instituto de Investigación en Matemáticas (IMUVa)Universidad de ValladolidValladolidSpain

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