CoxIter – Computing invariants of hyperbolic Coxeter groups

DOI10.1112/S1461157015000273zbMath1333.20040MaRDI QIDQ3465558

Rafael Guglielmetti

Publication date: 22 January 2016

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

zbMATH Keywords

invariants of hyperbolic Coxeter groups

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Discrete subgroups of Lie groups (22E40) Hyperbolic groups and nonpositively curved groups (20F67) Software, source code, etc. for problems pertaining to geometry (51-04) Software, source code, etc. for problems pertaining to group theory (20-04) Reflection groups, reflection geometries (51F15)

Related Items (11)

Hyperbolic Coxeter groups of minimal growth rates in higher dimensions ⋮ On commensurable hyperbolic Coxeter groups ⋮ Vinberg's algorithm for hyperbolic lattices ⋮ On minimal covolume hyperbolic lattices ⋮ The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume ⋮ Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups ⋮ Locally rigid right-angled Coxeter groups with Fuchsian ends in dimension \(5\) ⋮ All hyperbolic Coxeter \(n\)-cubes ⋮ Hyperbolic manifolds and pseudo-arithmeticity ⋮ CoxIter ⋮ Hyperbolic Coxeter groups and minimal growth rates in dimensions four and five

Cites Work

• On volumes of hyperbolic Coxeter polytopes and quadratic forms
• Hyperbolic reflection groups associated to the quadratic forms \(-3x_0^2+x_1^2+\cdots+x_n^2\).
• On the growth of cocompact hyperbolic Coxeter groups.
• The covolume of discrete subgroups of \(\mathrm{Iso}(\mathbb H^{2m})\)
• Automorphism groups of Lorentzian lattices
• Absence of crystallographic groups of reflections in Lobachevskij spaces of large dimension
• Commensurability classes of hyperbolic Coxeter groups.
• Hyperbolic Coxeter \(n\)-polytopes with \(n+2\) facets
• The classification of compact hyperbolic Coxeter \(d\)-polytopes with \(d+2\) facets
• The size of hyperbolic Coxeter simplex
• Hyperbolic orbifolds of minimal volume
• Foundations of Hyperbolic Manifolds
• Hyperbolic reflection groups
• THE ABSENCE OF DISCRETE REFLECTION GROUPS WITH NONCOMPACT FUNDAMENTAL POLYHEDRON OF FINITE VOLUME IN LOBACHEVSKY SPACE OF LARGE DIMENSION
• The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1
• On hyperbolic Coxeter n-polytopes with n + 2 facets
• ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS

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