Dissident maps on the seven-dimensional Euclidean space

A dissident map on a finite-dimensional euclidean vector space V isunderstood to be a linear map # : V#V #V such that v, w, #(v#w) arelinearly independent whenever v, w#V are. This notion of a dissidentmap provides a link between seemingly diverse aspects of real geometricalgebra, thereby revealing its shifting significance. While it generalizeson the one hand the classical notion of a vector product, it specializeson the other hand the structure of a real division algebra....