TY - JOUR
T1 - Cayley–Dickson split-algebras
T2 - Doubly alternative zero divisors and relation graphs
AU - Guterman, A. E.
AU - Zhilina, S. A.
N1 - Publisher Copyright:
© 2020, Lomonosov Moscow State University. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85129400593&partnerID=8YFLogxK
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AN - SCOPUS:85129400593
SN - 1560-5159
VL - 23
SP - 95
EP - 129
JO - Fundamental and Applied Mathematics
JF - Fundamental and Applied Mathematics
IS - 3
ER -