Geodesic
Trigonometrical algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 183-191

Voir la notice de l'article provenant de la source Math-Net.Ru

Euclidean $n$-dimensional spaces that have an analog of a vector product, i.e., a bilinear binary operation satisfying the identity $|x\cdot y|^2+(x,y)^2=|x|^2\cdot|y|^2$ ($(\cdot,\cdot)$ is a scalar product). It is clarified for which $n$ such a product exists. 
@article{ZNSL_1997_236_a20,
     author = {P. A. Terekhin},
     title = {Trigonometrical algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--191},
     publisher = {mathdoc},
     volume = {236},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a20/}
}
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P. A. Terekhin. Trigonometrical algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 183-191. http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a20/