Roots of unity in definite quaternion orders

@article{LuisArenas2015,
abstract = {A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of 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 type number 3 or larger. The proof extends to a few other closely related orders.},
author = {Luis Arenas-Carmona},
journal = {Acta Arithmetica},
keywords = {quaternion algebras; maximal orders; quotient graphs; selectivity},
language = {eng},
number = {4},
pages = {381-393},
title = {Roots of unity in definite quaternion orders},
url = {http://eudml.org/doc/286682},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Luis Arenas-Carmona
TI - Roots of unity in definite quaternion orders
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 4
SP - 381
EP - 393
AB - A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of 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 type number 3 or larger. The proof extends to a few other closely related orders.
LA - eng
KW - quaternion algebras; maximal orders; quotient graphs; selectivity
UR - http://eudml.org/doc/286682
ER -