关于最优嵌入和树
On optimal embeddings and trees
摘要：
本文将Bruhat-Tits树理论应用于研究二维和三维交换序到四元数代数的最优嵌入。具体来说，我们确定有多少共轭类的全球Eichler订单在四元数代数产生最佳表示等订单。这完成了C. Maclachlan，他只考虑平方自由能级和整环的Eichler阶作为子阶。同样的技术被用于本工作的第二部分，以计算本地嵌入数，扩展了J. Brzezinski以前的结果。
英文摘要：
We apply the theory of Bruhat-Tits trees to the study of optimal embeddings of two and three dimensional commutative orders into quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in a quaternion algebra yield optimal representations of such orders. This completes the previous work by C. Maclachlan, who considered only Eichler orders of square free level and integral domains as sub-orders. The same technique is used in the second part of this work to compute local embedding numbers, extending previous results by J. Brzezinski.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
