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arXiv · 1606.06396

On optimal embeddings and trees

Manuel Arenas·Luis Arenas-Carmona·Jaime Contreras
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Abstract

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.

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Manuel Arenas, Luis Arenas-Carmona, Jaime Contreras. 2016-06-21. On optimal embeddings and trees. https://arxiv.org/abs/1606.06396

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