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

2009/11/18 by Erik Darpö, Darpö, Erik, Abdellatif Rochdi +1
Mathematics · #17A35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17A35

paper · pdf · doi:10.48550/arxiv.0911.3570

16 pages

arxiv created 2009/11/18 · openalex publication_date 2009/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 dimension 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 characterised.

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