Hyperbolic reflection groups associated to the quadratic forms -3x₀² + x₁² + ... + x_n²

2010/07/14 by John Mcleod, Mcleod, John · 1 citation
Mathematics · #20F55 #20H15 #51F15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1007.2299

openalex publication_date 2010/07/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We determine the maximal hyperbolic reflection groups associated to the quadratic forms -3x₀² + x₁² + ... + x_n², n ≥ 2, and present the Coxeter schemes of their fundamental polyhedra. These groups exist in dimensions up to 13, and a proof is given that in higher dimensions these quadratic forms are not reflective.

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• Finiteness theorems for congruence reflection groups

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