Saved in:
Bibliographic Details
Main Author: Yang, Yuxuan
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.03661
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918484676444160
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