Given an order in a Quaternion algebra, determine if a type of maximal orders contains it

asked 2024-02-05 00:59:59 +0100

DrewC gravatar image

Let $B$ be a definite quaternion algebra over $\mathbb{Q}$ and $\mathcal{O}_0$ be an order. Given a maximal order $\mathcal{O}$ , how do we check if there exists a maximal order $\mathcal{O}' \cong \mathcal{O}$ containing $\mathcal{O}_0$? If it exists, can be enumerate all such maximal orders?

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