The Real Matrix Representations of Semi-Octonions
Öz
Rosenfeld’s book [6] is a wonderful introduction to the normed division algebras: the real numbers, the complex
numbers, the quaternions, and the octonions. A brief introduction of the semi-octonions is provided in this book. In
[3], we studied some fundamental properties of the semi-octonions, Os, and show that the set of unit semi-octonions
is a subgroup of Os. In this paper, we give a complete investigation to real matrix representations of semi-octonions,
and consider a relation between the powers of these matrices. The De Moivre's formula implies that there are
uncountably many matrices of the unit semi-octonions A satisfying An = I8 for every integer n ≥ 3.
numbers, the quaternions, and the octonions. A brief introduction of the semi-octonions is provided in this book. In
[3], we studied some fundamental properties of the semi-octonions, Os, and show that the set of unit semi-octonions
is a subgroup of Os. In this paper, we give a complete investigation to real matrix representations of semi-octonions,
and consider a relation between the powers of these matrices. The De Moivre's formula implies that there are
uncountably many matrices of the unit semi-octonions A satisfying An = I8 for every integer n ≥ 3.
Kaynakça
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