Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

DOI10.1070/IM8766zbMath1427.11064arXiv1903.08147MaRDI QIDQ3120452

N. V. Bogachev

Publication date: 4 March 2019

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.08147

zbMATH Keywords

rootsreflection groupsfundamental polyhedrareflective hyperbolic lattices

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Quadratic forms over global rings and fields (11E12) Reflection groups, reflection geometries (51F15) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items (3)

Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes ⋮ From geometry to arithmetic of compact hyperbolic Coxeter polytopes ⋮ Classification of stably reflective hyperbolic \(\mathbb{Z}[\sqrt 2 \)-lattices of rank 4]

Uses Software

• GitHub
• vinberg-algorithm

Cites Work

• On the maximal dimension of Lorentz lattices with cofinite reflection group
• Finiteness of arithmetic hyperbolic reflection groups
• Geometry II: spaces of constant curvature. Transl. from the Russian by V. Minachin
• Vinberg's algorithm for hyperbolic lattices
• Reflective Lorentzian lattices of signature \((5,1)\)
• Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections. Algebro-geometric applications
• Reflection groups of the quadratic form \(-px_0^2+x_1^2+\dots+x_n^2\) with \(p\) prime.
• Arithmetic hyperbolic reflection groups
• Classification of $2$-reflective hyperbolic lattices of rank $4$
• Hyperbolic reflection groups
• ON ARITHMETIC GROUPS GENERATED BY REFLECTIONS IN LOBACHEVSKY SPACES
• ON THE CLASSIFICATION OF ARITHMETIC GROUPS GENERATED BY REFLECTIONS IN LOBACHEVSKY SPACES
• Reflective anisotropic hyperbolic lattices of rank 4
• The reflective Lorentzian lattices of rank 3
• Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
• ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS
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