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

2026/02/28 by Maximilian Illmer
Mathematics · #math.LO

paper · pdf

18 pages

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

We build on our previous paper \citeconstructive 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 \citesavi.

Citations

• Constructive Quantifier Elimination with a Focus on Matrix Rings
• On the first-order theories of quaternions and octonions
• Smooth functions invariant under the action of a compact lie group