Leonie Scheeren - The Voronoi Algorithm for calculating unit groups: Summer School 2022 - Cohomology, Geometry and Explicit Number Theory

HAL (Le Centre pour la Communication Scientifique Directe)

Abstract

Following an algorithm by Coulangeon, Nebe, Braun and Schönnenbeck to compute unit groups of orders in finite simple Q-algebras, we will again talk about the Voronoi algorithm for finding perfect forms. In this case we will work with a generalized version by Opgenorth in the context of dual cones and consider a combination with Bass-Serre theory regarding groups acting on trees via automorphisms, which yields information about the structure of said unit groups, which will be acting on a Voronoi-graph. In particular we are going to focus on finding unit groups of maximal orders in indefinite Quaternion algebras over Q and compute an example.

Authors 2

1. Leonie Sheeren Aachen

   RWTH Aachen University · Universitätsklinikum Aachen

   Affiliation as printed

   UKA - Universitätsklinikum RWTH Aachen - University Hospital Aachen [Aachen, Germany] (Universitätsklinikum Aachen, AöR -Pauwelsstraße 30 -52074 Aachen - Germany)

2. Fanny Bastien

   Institut Fourier

   Affiliation as printed

   IF - Institut Fourier (100, rue des maths 38610 Gières - France)