Subalgebras of the Split Octonions

Bentz, Lida; Dray, Tevian

doi:10.1007/s00006-018-0859-6

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Definition 327 a Mapping φ1

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Cited by 7 publications

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“…• The complex numbers (C), the quaternions (H), the octonions (O), and the sedenions (S) are the algebras of the main sequence for n = 1, 2, 3, and 4, correspondingly. We refer the reader to [6] for the definition of H and O, and to [13] for that of S. • The split-complex numbers ( Ĉ), the split-quaternions (the coquaternions; Ĥ), and the splitoctonions (the hyperbolic octonions; Ô) are the examples of real low-dimensional split-algebras, all of them being defined in [10].…”

Section: Definition 327 a Mapping φmentioning

confidence: 99%

Cayley–Dickson Split-Algebras: Doubly Alternative Zero Divisors and Relation Graphs

Guterman

Zhilina

2023

J Math Sci

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Our paper is devoted to the investigations of doubly alternative zero divisors of the real Cayley-Dickson split-algebras. We describe their annihilators and orthogonalizers and also establish the relationship between centralizers and orthogonalizers for such elements. Then we obtain an analogue of the real Jordan normal form in the case of the split-octonions. Finally, we describe commutativity, orthogonality, and zero divisor graphs of the split-complex numbers, the split-quaternions, and the split-octonions in terms of their diameters and cliques.

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Section: Definition 327 a Mapping φmentioning

confidence: 99%