Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields

Yuxuan Yang

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arXiv · 2605.03661

Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields

Yuxuan Yang

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Abstract

Let $B$ be a central simple algebra of degree 3 over a number field $F$ and $K/F$ be a finite extension of degree 3. For an order $S$ of $K$, we determine exactly when $S$ cannot be optimally embedded into all maximal orders of $B$. Moreover, we further determine exactly when $S$ can be optimally embedded into $\frac{1}{3}$ isomorphism classes of maximal orders of $B$ and $\frac{2}{3}$ isomorphism classes of maximal orders of $B$ in the rest of cases.

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Yuxuan Yang. 2026-05-05. Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields. https://arxiv.org/abs/2605.03661

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