Roots of unity in definite quaternion orders
Number Theory
2014-04-15 v1
Abstract
A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with a type number 3 or larger. The proof extends to a few other closely related orders.
Keywords
Cite
@article{arxiv.1404.3244,
title = {Roots of unity in definite quaternion orders},
author = {Luis Arenas-Carmona},
journal= {arXiv preprint arXiv:1404.3244},
year = {2014}
}