# Dissident maps on the seven-dimensional Euclidean space

Ernst Dieterich; Lars Lindberg

Colloquium Mathematicae (2003)

- Volume: 97, Issue: 2, page 251-276
- ISSN: 0010-1354

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topErnst 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 -

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