Work

On linear equations over split-octonions

Year: 2026

Type: article

Abstract: Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations (ax)b=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.

Source: Electronic Journal of Linear Algebra

DOI: 10.13001/ela.2026.10099

Authors: Artem Lopatin, Alexandr Zubkov

Institutions: Universidade Estadual de Campinas (UNICAMP), Sobolev Institute of Mathematics

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404407736

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