Computing quaternion quotient graphs via representation of orders

2012/07/15 by Luis Arenas-Carmona, Arenas-Carmona, Luis · 1 citation
Computer Science · Engineering · Mathematics · #11R58-11R54 (Primary) 11R65-20H25-20E08-14C20 (Secondary) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11R58-11R54 #msc:11R65-20H25-20E08-14C20

paper · pdf · doi:10.48550/arxiv.1207.3470

24 pages

arxiv created 2012/07/15 · openalex publication_date 2012/07/15 · arxiv updated 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the correspondence assigning the vertices of a certain quotient of the local Bruhat-Tits tree for the general linear group over a global function field, to conjugacy classes of maximal orders in some quaternion algebras. The interplay between quotient graphs and orders can be used to study representation of orders if the quotient graphs are known and conversely. We use this converse to find a reciprocity law between quotient graph at diferent places that suffices to compute, recursively, all local quotient graphs for a matrix algebra over a rational function field.

Cited by

• Representation field for orders of small ranks

Related

• On the missing branches of the Bruhat-Tits tree
• On some branches of the Bruhat-Tits tree
• On optimal embeddings and trees
• Branches in the Bruhat-Tits tree for local fields of even characteristic
• Trees, quaternion algebras and modular curves