Relation Graphs of the Sedenion Algebra

A. E. Guterman, S. A. Zhilina

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let S denote the algebra of sedenions and let ΓO(S) denote its orthogonality graph. One can observe that every pair of zero divisors in S generates a double hexagon in ΓO(S). The set of vertices of a double hexagon can be extended to a basis of S that has a convenient multiplication table. The set of vertices of an arbitrary connected component of ΓO(S) is described, and its diameter is found. Then, the bijection between the connected components of ΓO(S) and the lines in the imaginary part of the octonions is established. Finally, the commutativity graph of the sedenions is considered, and it is shown that all the elements whose imaginary part is a zero divisor belong to the same connected component, and its diameter lies in between 3 and 4.

Original languageEnglish
Pages (from-to)254-270
Number of pages17
JournalJournal of Mathematical Sciences
Volume255
Issue number3
DOIs
StatePublished - Jun 2021
Externally publishedYes

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© 2021, Springer Science+Business Media, LLC, part of Springer Nature.

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