Geodesic
On the Cayley--Dickson process for dialgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2110-2123

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We prove that the dialgebras, which are obtained by the Cayley–Dickson process from the two-dimensional commutative associative dialgebra ${\mathcal D}$, are disimple noncommutative Jordan dialgebras. Furthermore, a decomposition holds for them into the direct sum of a composition algebra and the equating ideal of the dialgebra.
Keywords: Cayley–Dickson process, flexible algebra, involution, noncommutative Jordan algebra
Mots-clés : dialgebra, disimple dialgebra, composition algebra. 
@article{SEMR_2019_16_a36,
     author = {A. P. Pozhidaev},
     title = {On the {Cayley--Dickson} process for dialgebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2110--2123},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a36/}
}
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A. P. Pozhidaev. On the Cayley--Dickson process for dialgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2110-2123. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a36/