On the Octonion-like Associative Division Algebra

Juhi Khalid; Martin Bouchard

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arXiv · 2012.11359

On the Octonion-like Associative Division Algebra

Juhi Khalid·Martin Bouchard

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Abstract

Using elementary linear algebra, this paper clarifies and proves some concepts about a recently introduced octonion-like associative division algebra over R. This octonion-like algebra is actually the same as the split-biquaternion algebra, an even subalgebra of Clifford algebra Cl(4,0). For two seminorms described in the paper, it is shown that the octonion-like algebra is a seminormed composition algebra over R. Moreover, additional results related to the computation of inverse numbers in the octonion-like algebra are introduced, showing that the octonion-like algebra is a seminormed division algebra over R, i.e., division by any number is possible as long as the two seminorms are non-zero. Additional results on normalization of octonion-like numbers and some involutions are also presented. The elementary linear algebra descriptions used in the paper also allow straightforward software implementations of the octonion-like algebra.

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Juhi Khalid, Martin Bouchard. 2020-12-18. On the Octonion-like Associative Division Algebra. https://arxiv.org/abs/2012.11359

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