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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03661 |
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| _version_ | 1866918484676444160 |
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| author | Yang, Yuxuan |
| author_facet | Yang, Yuxuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03661 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields Yang, Yuxuan Number Theory 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. |
| title | Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.03661 |