Dissident maps on the seven-dimensional Euclidean space

• Autorzy: Ernst Dieterich , Lars Lindberg
• Języki publikacji: EN

Abstrakty

EN

Our article contributes to the classification of dissident maps on ℝ ⁷, which in turn contributes to the classification of 8-dimensional real division algebras.
We study two large classes of dissident maps on ℝ ⁷. The first class is formed by all composed dissident maps, obtained from a vector product on ℝ ⁷ by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures of those 8-dimensional real quadratic division algebras which arise from a 4-dimensional real quadratic division algebra by doubling. For each of these two classes we exhibit a complete (but redundant) classification, given by a 49-parameter family of composed dissident maps and a 9-parameter family of doubled dissident maps respectively. The intersection of these two classes forms one isoclass of dissident maps only, namely the isoclass consisting of all vector products on ℝ ⁷.

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 17A45: Quadratic algebras (but not quadratic Jordan algebras)
• 17A35: Division algebras
• 15A30: Algebraic systems of matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 2
• Strony: 251-276

Daty

wydano

2003

Twórcy

autor

Ernst Dieterich

• Matematiska institutionen, Uppsala universitet, Box 480, SE-751 06 Uppsala, Sweden

autor

Lars Lindberg

• Matematiska institutionen, Uppsala universitet, Box 480, SE-751 06 Uppsala, Sweden

Identyfikatory

DOI

10.4064/cm97-2-10