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

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.

16 pages

References in corpus (2)

• Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation
• The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5

Cited by in corpus (2)

• Non-associative algebraic structures: classification and structure
• Partially Alternative Algebras