On the limit set of root systems of Coxeter groups acting on Lorentzian spaces

DOI10.1080/00927872.2019.1684503zbMath1479.20029arXiv1305.0052OpenAlexW2984394643MaRDI QIDQ5220634

Christophe Hohlweg, Vivien Ripoll, Jean-Philippe Préaux

Publication date: 27 March 2020

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0052

zbMATH Keywords

Coxeter grouproot systemKleinian groupshyperbolic Coxeter groupApollonian gaskethyperbolic isometriesLorentzian spacediscrete reflection grouplimit rootslimit set of discrete group

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Reflection groups, reflection geometries (51F15) Root systems (17B22)

Related Items (3)

\(n\)-low elements and maximal rank \(k\) reflection subgroups of Coxeter groups ⋮ Imaginary cones and limit roots of infinite Coxeter groups ⋮ Lorentzian Coxeter systems and Boyd-Maxwell ball packings

Cites Work

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• Imaginary cones and limit roots of infinite Coxeter groups
• Coxeter groups, imaginary cones and dominance.
• Sphere packings and hyperbolic reflection groups
• Apollonian circle packings: Geometry and group theory. I: The Apollonian group
• The conjugacy problem for Coxeter groups.
• Lectures on hyperbolic geometry
• Discrete groups generated by reflections
• Limit directions for Lorentzian Coxeter systems
• Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
• The Modular Surface and Continued Fractions
• Foundations of Hyperbolic Manifolds
• Buildings
• A Tale of Two Fractals
• DISTRIBUTION OF ACCUMULATION POINTS OF ROOTS FOR TYPE (n - 1, 1) COXETER GROUPS
• Imaginary cone and reflection subgroups of Coxeter groups
• Asymptotical Behaviour of Roots of Infinite Coxeter Groups
• Reflection groups in algebraic geometry
• The Apollonian Packing of Circles

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