Roots of unity in definite quaternion orders

2014/04/11 by Arenas-Carmona, Luis
#11R52-16G30 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1404.3244

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.

Related

• Selectivity on division algebras
• Constructing non-maximal orders in quaternion algebras
• Selectivity in Quaternion Algebras
• Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields
• Optimal spinor selectivity for quaternion Bass orders