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Fundamentalnaya i Prikladnaya Matematika, 2020, Volume 23, Issue 3, Pages 95–129
(Mi fpm1900)
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This article is cited in 4 scientific papers (total in 4 papers)
Cayley–Dickson split-algebras: Doubly alternative zero divisors and relation graphs
A. E. Gutermanabc, S. A. Zhilinaac a Lomonosov Moscow State University, Moscow, 119991, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia
c Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia
Abstract:
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.
Citation:
A. E. Guterman, S. A. Zhilina, “Cayley–Dickson split-algebras: Doubly alternative zero divisors and relation graphs”, Fundam. Prikl. Mat., 23:3 (2020), 95–129; J. Math. Sci., 269:3 (2023), 331–355
Linking options:
https://www.mathnet.ru/eng/fpm1900 https://www.mathnet.ru/eng/fpm/v23/i3/p95
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Abstract page: | 164 | Full-text PDF : | 58 | References: | 17 |
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