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arXiv · 2602.21326

Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras

Maximilian Illmer
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Abstract

We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other classes of finite-dimensional algebras over real closed and algebraically closed fields. In particular, the first two examples answer an open question posed recently in \cite{savi}.

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Maximilian Illmer. 2026-02-24. Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras. https://arxiv.org/abs/2602.21326

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