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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 472, Pages 44–75
(Mi znsl6639)
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This article is cited in 6 scientific papers (total in 6 papers)
Relation graphs of real Cayley–Dickson algebras
A. E. Gutermanab, S. A. Zhilinaa a Lomonosov Moscow State University, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
Abstract:
The paper presents anticommutativity conditions for elements of arbitrary real Cayley–Dickson algebras, based on which the anticommutativity graphs on equivalence classes of such algebras are classified. Under some additional conditions on the algebras considered, an expression for the centralizer of an element in terms of its orthogonalizer is obtained. Conditions sufficient for this interrelation to hold are provided. Also examples of real Cayley–Dickson algebras in which the centralizer and orthogonalizer of an element are not interrelated in this way are considered.
Key words and phrases:
Cayley–Dickson algebras, anticommutativity, anticommutativity graphs, relation graphs, centralizer, orthogonalizer.
Received: 01.11.2018
Citation:
A. E. Guterman, S. A. Zhilina, “Relation graphs of real Cayley–Dickson algebras”, Computational methods and algorithms. Part XXXI, Zap. Nauchn. Sem. POMI, 472, POMI, St. Petersburg, 2018, 44–75
Linking options:
https://www.mathnet.ru/eng/znsl6639 https://www.mathnet.ru/eng/znsl/v472/p44
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Abstract page: | 132 | Full-text PDF : | 48 | References: | 19 |
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