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Classification of the four-dimensional power-commutative real division algebras*

Published online by Cambridge University Press:  15 November 2011

Erik Darpö  and
Abdellatif Rochdi
Erik Darpö
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom ([email protected])
Abdellatif Rochdi
Affiliation:
Département de Mathématiques et Informatique, Faculté des Sciences, Ben M'Sik, Université Hassan II Mohammedia, 7955 Casablanca, Morocco ([email protected])
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Abstract

A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative real division algebra is an isotope of a particular kind of a quadratic division algebra. The description of such isotopes in dimensions four and eight is reduced to the description of quadratic division algebras. In dimension four, this leads to a complete and irredundant classification. As a special case, the finite-dimensional power-commutative real division algebras that have a unique non-zero idempotent are characterized.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 6 , December 2011 , pp. 1207 - 1223
Copyright
Copyright © Royal Society of Edinburgh 2011

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References

* This paper is dedicated to the memory of Nadia Benhoussa.