Relation graphs of the split-sedenion algebra (Q2202834)

In this paper, the author presents the Cayley-Dickson split-sedenion algebra, an algebra of dimension 16. The author studies the zero divisors of the Cayley-Dickson split-sedenion algebra and classifies them by using the dimensions of their annihilators and orthogonalizers. Based on the obtained results, the orthogonality graph and the zero divisor graph of the split-sedenions are described by using their diameters and cliques. The paper has four sections. First section presents some introductory notions. In Section 2 the Cayley-Dickson process and some examples and properties of obtained algebras are presented. In Section 3 and Section 4 are obtained the main results.