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arXiv · 2411.08500

On linear equations over split-octonions

Artem Lopatin·Alexandr N. Zubkov
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Abstract

Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations $a(xb)=c$ and $a(bx)=c$ over the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial equations in the split-octonions. Moreover, we show that if a linear monomial equation over the split-octonions with nonzero constant term has at least two solutions, then it necessarily possesses an invertible solution.

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Artem Lopatin, Alexandr N. Zubkov. 2024-11-13. On linear equations over split-octonions. https://arxiv.org/abs/2411.08500

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