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  • 1.
    Darpö, Erik
    et al.
    University of Oxford.
    Rochdi, Abdellatif
    Université Hassan II Mohammedia, Morocco.
    Classification of the four-dimensional power-commutative real division algebras2011In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 141, no 6, p. 1207-1223Article in journal (Refereed)
    Abstract [en]

    A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative realdivision 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-dimensionalpower-commutative real division algebras that have a unique non-zero idempotent are characterized.

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