Relation Graphs of the Sedenion Algebra
| Autor: | Svetlana Zhilina, Alexander Guterman |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Connected component Applied Mathematics General Mathematics 010102 general mathematics Sedenion Basis (universal algebra) Multiplication table 01 natural sciences 010305 fluids & plasmas Algebra Orthogonality 0103 physical sciences Bijection 0101 mathematics Commutative property Zero divisor Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 255:254-270 |
| ISSN: | 1573-8795 1072-3374 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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