Automorphism Groups of Hyperbolic Lattices

TL;DR

This paper presents an algorithm to compute the automorphism group of hyperbolic lattices using dual cones, advancing the understanding of lattice symmetries in hyperbolic geometry.

Contribution

It introduces a novel algorithm leveraging dual cones to efficiently generate automorphism groups of hyperbolic lattices.

Findings

Algorithm successfully computes automorphism groups for various hyperbolic lattices.

Provides a new computational method based on dual cones.

Enhances tools for studying symmetries in hyperbolic lattice structures.

Abstract

Based on the concept of dual cones introduced by J.Opgenorth we give an algorithm to compute a generating system of the group of automorphisms of a lattice endowed with a hyperbolic bilinear form.