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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-10,
author = {Ernst Dieterich and Lars Lindberg},
title = {Dissident maps on the seven-dimensional Euclidean space},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {251-276},
zbl = {1056.17001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-10}
}
Ernst Dieterich; Lars Lindberg. Dissident maps on the seven-dimensional Euclidean space. Colloquium Mathematicae, Tome 96 (2003) pp. 251-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-10/