A note on the real division algebras with non-trivial derivations

Diabang, Andre S.; Diankha, Oumar; Ly, M.; Rochdi, A.

doi:10.12988/ija.2016.51167

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2018

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Cited by 4 publications

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“…In [6], another approach has been proposed for the study of a RDA using its Lie algebra of derivations. This approach leads to some partial results [7,34,23,31,16,2]. One can also find some studies in dimension 4 in [10, (15.7), p. 179] and [3,4,38].…”

Section: Introductionmentioning

confidence: 84%

Embedding problems for real division algebras

Mekrami¹,

Rochdi²

2018

ija

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By using the well-known processes of isotopy and Cayley-Dickson duplication, we plunge every two-dimensional real division algebra into an algebra isotopic to H and every real division algebra isotopic to H into an algebra isotopic to O. Also these processes permit us to show that every four-dimensional real power commutative division algebra, not necessarily isotopic to H, can be embedded into an eight-dimensional real division algebra which is power commutative. This partially answers a question asked in J. Algebra 282 (2004), 758-796. Such an embedding is refined in a way to provide examples where the triviality of the Lie algebra of derivations is preserved.

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