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2 edition of Discrete complex reflection groups found in the catalog.

Discrete complex reflection groups

V. L. Popov

Discrete complex reflection groups

by V. L. Popov

  • 287 Want to read
  • 30 Currently reading

Published by Mathematical Institute-Library in Utrecht, The Netherlands .
Written in English

    Subjects:
  • Discrete groups.,
  • Group theory -- Generators.

  • Edition Notes

    StatementV.L. Popov.
    SeriesCommunications of the Mathematical Institute Rijksuniversiteit Utrecht -- 15-1982., Communications of the Mathematical Institute -- 15.
    ContributionsRijksuniversiteit te Utrecht. Mathematisch Instituut.
    Classifications
    LC ClassificationsQA171 .P66 1982
    The Physical Object
    Pagination88 p. :
    Number of Pages88
    ID Numbers
    Open LibraryOL16134945M

    Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently been discovered that complex reflection groups play a key role in the theory.   A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex s: 1.

    L. Wang, Simple root systems and presentations for the primitive complex reflection groups generated by involutive reflections, Master thesis in ECNU (). Google Scholar; P. Zeng, Simple root systems and presentations for the primitive complex reflection groups containing reflections of order > 2, Master thesis in ECNU (). Google Scholar.   They look at complex hyperbolic lattices, rank-one isometries of proper CAT(0)-spaces, trace polynomials for simple loops on the twice punctured torus, the simplicial volume of products and fiber bundles, the homology of Hantzsche-Wendt groups, Seifert fibered structure and rigidity on real Bott towers, exotic circles in groups of piecewise.

    Discrete groups of reflections in the complex ball O. V. Shvartsman Functional Analysis and Its Applications vol pages 81 – 83 () Cite this article. In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.. Complex reflection groups arise in the study of the invariant theory of polynomial the midth century, they were completely classified in work of Shephard and Todd.


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Discrete complex reflection groups by V. L. Popov Download PDF EPUB FB2

Discrete complex reflection groups. we shall find all the non-congruent presentations of the complex reflection group G 12 by generators and relations according to the results in among the S k. Discrete complex reflection groups.

Book April extended the idea of root systems to complex reflection groups giving explicitly root systems for all dimensions greater than two. M C. Discrete complex reflection groups. Utrecht, The Netherlands: Mathematical Institute-Library, [] (OCoLC) Document Type: Book: All Authors / Contributors: V L Popov; Rijksuniversiteit te Utrecht.

Mathematisch Instituut. The book is divided into three parts. The first part, consisting of Chap tersis concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma.

CONTINUOUS AND DISCRETE SYMMETRY Reflection groups are discrete: one cannot move a symmetry a small amount and obtain a new symmetry. For example in any of the examples above, moving an axis of symmetry a small amount never results in a new axis of symmetry.

An example of a group which does not have this property is the group of symmetries. We investigate Steinberg's regularity theorem for affine complex reflection groups, analogs of affine Weyl groups called crystallographic complex reflection groups.

These discrete groups were classified by Popov [12] in and are generated by reflections about affine hyperplanes, i.e., mirrors that do not necessarily include the : Philip Puente, Anne V.

Shepler. Topology Vol. 25, No. 2, pp. ,86 Printed in Great Britain. Pergamon Press Ltd. GRAPHS ATTACHED TO CERTAIN COMPLEX HYPERBOLIC DISCRETE Discrete complex reflection groups book GROUPS MASAAKI YOSHIDA (Received 31 October ) INTRODUCTION IN THE last few years, several discrete (complex) reflection groups acting on the unit ball B.

Mostow [19] used it brilliantly to construct several discrete groups of motions of the complex hyperbolic plane. However, in Lobachevsky spaces of dimensions > 3 this method was used successfully only for groups generated by reflections with respect to hyperplanes (so-called reflection groups) and to its subgroups of finite index.

This book is about connections between groups and geometry. We begin by considering groups of isometries of Euclidean space generated by hyperplane reflections. replacing “finite” by “discrete” and “linear” by “affine”.

Keywords Root System Brown K.S. () Finite Reflection Groups. In: Buildings. Springer, New York, NY. OVER DISCRETE COMPLEX REFLECTION GROUPS APOORVA KHARE Abstract.

We de ne and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (), we con-struct the rst examples of such nite-dimensional algebras that are not the ‘usual’ nil-Coxeter algebras: a novel 2-parameter type A family that we.

Chapter II. Crystallographic reflection groups in Lobachevskii spaces § 5. The language of Coxeter schemes.

Construction of crystallographic reflection groups § 6. The non-existence of discrete reflection groups with bounded fundamental polytope in higher-dimensional Lobachevskii spaces References.

REFLECTION GROUPS IN ALGEBRAIC GEOMETRY IGOR V. DOLGACHEV To Ernest Borisovich Vinberg Abstract. After a brief exposition of the theory of discrete reflection groups in spherical, euclidean and hyperbolic geometry as well as their analogs in complex spaces we present a survey of appearances of these groups in various areas of algebraic.

REFLECTION GROUPS IN ALGEBRAIC GEOMETRY 5 Let G be the group generated by the two reflections s 1,s assume that H 1 = H 2, i.e. s 1 = s following two cases may occur: Case 1: The angle φ is of the form nπ/m for some rational number r = n/m.

In the following we assume that m = ∞ if φ =0. In this case s 2s 1 is the rotation about the angle 2nπ/m and hence (s2s 1. This is the book on a newly emerging field of discrete differential geometry.

It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. ( views) Lists, Decisions, and Graphs. Title: Generalized nil-Coxeter algebras over discrete complex reflection groups.

Authors: Apoorva Khare (Submitted on 29 Janlast revised 22 Jan (this version, v5)) Abstract: We define and study generalized nil-Coxeter algebras associated to Coxeter groups.

Motivated by a question of Coxeter (), we construct the first examples. [brouelnm] M. Broué, Introduction to Complex Reflection Groups and their Braid Groups, New York: Springer-Verlag,vol.

Show bibtex @book{brouelnm, mrkey = {}. The book will serve graduate students as well as researchers." (L'Enseignement Mathématique, Vol. 51 (), ) "The general theory of Coxeter groups naturally involves combinatorics, geometry and algebra.

The aim of the book under review is to present the core combinatorial aspects of the theory of Coxeter groups. Reviews: 1. properties of flnite Coxeter groups (center of the braid group, construction of Hecke algebras). Background from complex reflection groups For all the results quoted here, we refer the reader to the classical literature on complex re°ections groups, such as [Bou], [Ch], [Co], [ShTo], [Sp], and also to the.

adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A. This important work is at the crossroads of several branches of mathematics, including hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis.

The main focus throughout is on the 'Big Monster,' that is, on Thurston's Hyperbolization Theorem, which has completely changed the landscape of 3-dimensional topology and Kleinian group theory. most important semigroups are groups. De nition A group (G;) is a set Gwith a special element e on which an associative binary operation is de ned that satis es: 1.

ea= afor all a2G; every a2G, there is an element b2Gsuch that ba= e. Example Some examples of groups. integers Z under addition +. set GL.A discrete group of transformations generated by reflections in hyperplanes. The most frequently studied are those consisting of mappings of a simply-connected complete Riemannian manifold of constant curvature, i.e.

of a Euclidean space $ E ^ {n} $, a sphere $ S ^ {n} $ or a hyperbolic (Lobachevskii) space $ \Lambda ^ {n} $.Get this from a library! Discrete Groups and Geometry.

[W J Harvey; C Maclachlan;] -- Proceedings of the conference held at the University of Birmingham in honour of Professor A.M.

Macbeath. Many interesting papers are included from respected figures, on discrete group theory.