The reflective Lorentzian lattices of rank 3

DOI10.1090/S0065-9266-2012-00648-4zbMath1302.11046arXiv1010.0486OpenAlexW4214667309MaRDI QIDQ5403710

Daniel Allcock

Publication date: 18 March 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0486

zbMATH Keywords

Weyl groupCoxeter groupLorentzian latticeVinberg's algorithm

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Discrete subgroups of Lie groups (22E40) Automorphism groups of lattices (11H56)

Related Items (11)

Vinberg's algorithm for hyperbolic lattices ⋮ The classification of rank 3 reflective hyperbolic lattices over ⋮ Automorphism groups of hyperbolic lattices ⋮ From geometry to arithmetic of compact hyperbolic Coxeter polytopes ⋮ The reflective Lorentzian lattices of rank 3 ⋮ Bounds for arithmetic hyperbolic reflection groups in dimension 2 ⋮ Reflective Lorentzian lattices of signature \((5,1)\) ⋮ The Conway-Sloane calculus for 2-adic lattices ⋮ Arithmetic hyperbolic reflection groups ⋮ Virtually special embeddings of integral Lorentzian lattices ⋮ Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

Uses Software

• PARI/GP

Cites Work

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• Transformations of a quadratic form which do not increase the class-number II
• World-structure and non-Euclidean honeycombs

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