Symmetry 2024, 16(12), 1567; https://doi.org/10.3390/sym16121567 - 22 Nov 2024
Abstract
This article focuses on generalized octonions which include real octonions, split octonions, semi octonions, split semi octonions, quasi octonions, split quasi octonions and para octonions in special cases. We make a classification according to the inner product and vector parts and give the
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This article focuses on generalized octonions which include real octonions, split octonions, semi octonions, split semi octonions, quasi octonions, split quasi octonions and para octonions in special cases. We make a classification according to the inner product and vector parts and give the polar forms for lightlike generalized octonions. Furthermore, the matrix representations of the generalized octonions are given and some properties of these representations are achieved. Also, powers and roots of the matrix representations are presented. All calculations in the article are achieved by using MATLAB R2023a and these codes are presented with an illustrative example.
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(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)
