2011/10/02 by Luis Arenas-Carmona, Arenas-Carmona, Luis
Mathematics · #11R37 #11R52 #11R56 #16G10 #16G30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1110.0233
openalex publication_date 2011/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If H and D are two orders in a central simple algebra A with D of maximal rank and containing H, the theory of representation fields describes the set of spinor genera of orders in the genus of D representing the order H. When H is contained in a maximal subfield of A and the dimension of A is the square of a prime p, the proportion of spinor genera representing H has the form r/p, in fact, when the representation field exists, this proportion is either 1 or 1/p. In the later case the order H is said to be selective for the genus. The condition for selectivity is known when D is maximal and also when p = 2 and D is an Eichler order. In this work we describe the orders H that are selective for at least one genus of orders of maximal rank in A.