Dissident maps on the seven-dimensional Euclidean space

Ernst Dieterich, and Lars Lindberg. "Dissident maps on the seven-dimensional Euclidean space." Colloquium Mathematicae 97.2 (2003): 251-276. <http://eudml.org/doc/285069>.

@article{ErnstDieterich2003,
abstract = { 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. },
author = {Ernst Dieterich, Lars Lindberg},
journal = {Colloquium Mathematicae},
keywords = {dissident map; real quadratic division algebra; doubling functor; collineation; configuration; classification},
language = {eng},
number = {2},
pages = {251-276},
title = {Dissident maps on the seven-dimensional Euclidean space},
url = {http://eudml.org/doc/285069},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Ernst Dieterich
AU - Lars Lindberg
TI - Dissident maps on the seven-dimensional Euclidean space
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 2
SP - 251
EP - 276
AB - 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.
LA - eng
KW - dissident map; real quadratic division algebra; doubling functor; collineation; configuration; classification
UR - http://eudml.org/doc/285069
ER -