Spherical simplices generating discrete reflection groups
نویسندگان
چکیده
منابع مشابه
Euclidean simplices generating discrete reflection groups
Let P be a convex polytope in the spherical space S, in the Euclidean space E, or in the hyperbolic space H. Consider the group GP generated by reflections in the facets of P . We call GP a reflection group generated by P . The problem we consider in this paper is to list polytopes generating discrete reflection groups. The answer is known only for some combinatorial types of polytopes. Already...
متن کاملOn finite index reflection subgroups of discrete reflection groups
Let G be a discrete group generated by reflections in hyperbolic or Euclidean space, and H ⊂ G be a finite index subgroup generated by reflections. Suppose that the fundamental chamber of G is a finite volume polytope with k facets. In this paper, we prove that the fundamental chamber of H has at least k facets. 1. Let X be hyperbolic space H, Euclidean space E or spherical space S . A polytope...
متن کاملThe local recognition of reflection graphs of spherical Coxeter groups
Based on the third author’s thesis (arXiv:0805.2403) in this article we complete the local recognition of commuting reflection graphs of spherical Coxeter groups arising from irreducible crystallographic root systems.
متن کاملGeneralized Nil-coxeter Algebras over Discrete Complex Reflection Groups
We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the ‘usual’ nil-Coxeter algebras: a novel 2-parameter type A family that we call NCA(n, d). We explore several combinatorial properties of NCA(n, d), including its Coxeter word basis, length...
متن کاملThe Deformation Theory of Discrete Reflection Groups and Projective Structures
We study deformations of discrete groups generated by linear reflections and associated geometric structures on orbifolds via cohomology of Coxeter groups with coefficients in the adjoint representation associated to a discrete representation. We completely describe a cochain complex that computes this cohomology for an arbitrary discrete reflection group and, as a consequence of this descripti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Sbornik: Mathematics
سال: 2004
ISSN: 1064-5616,1468-4802
DOI: 10.1070/sm2004v195n04abeh000816