Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910055857651712 |
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| author | Illmer, Maximilian |
| author_facet | Illmer, Maximilian |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21326 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras Illmer, Maximilian Logic 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}. |
| title | Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2602.21326 |