Four-Dimensional Real Third-Power Associative Division Algebras

Diankha, Oumar; Traoré, M.; Ramírez, Maribel; Rochdi, A.

doi:10.1080/00927872.2015.1065865

Cited by 6 publications

(1 citation statement)

References 21 publications

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“…However, the classification of RDA of dimension d = 4 or 8 is still an open problem and we have only some partial results. Indeed, (1) for d = 4, we have a classification of absolute-valued algebras [33,36,12], and power-commutative RDA [15,18], including both quadratic RDA [30,20,22] and flexible RDA [29,8,13,14], (2) the case d = 8 is more difficult and there is only a classification of absolute-valued algebras [35,11] and flexible RDA [29,8,13,14].…”

Section: Introductionmentioning

confidence: 99%

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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