Reflection groups | Coxeter groups

Reflection group

In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a discrete group, and is generally considered separately. (Wikipedia).

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Light and Optics 1_2 Introduction to Reflection

Reflection form plane and spherical mirrors

From playlist Physics - Light and Optics

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Light and Optics 1_3 Introduction to Reflection

Reflection from plane and spherical mirrors.

From playlist Physics - Light and Optics

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Bireflections (Geometric Algebra 1.3)

In the third video of the series we need to have a chat about reflections. They are the atoms of transformations: a single reflection is a discrete transformation of space, but the product of two reflections is a continuous transformation. When the two reflections intersect they generate a

From playlist Bivector.net

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Light and Optics 3_1 More on Reflection and Refraction

A more in depth look at reflection and refraction.

From playlist Physics - Light and Optics

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Sabyasachi Mukherjee: Interbreeding in conformal dynamics, and its applications near and far

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

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Visual Group Theory, Lecture 2.2: Dihedral groups

Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota

From playlist Visual Group Theory

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Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups

24th Workshop in Geometric Topology, Calvin College, June 29, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

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Vic Reiner, Lecture II - 11 February 2015

Vic Reiner (University of Minnesota) - Lecture II http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open questions

From playlist Algebraic topology, geometric and combinatorial group theory - 2015

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Dihedral Groups -- Abstract Algebra 4

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From playlist Abstract Algebra

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Physics 11.1.1a - Reflection

First video in a series on reflection and refraction.

From playlist Physics - Reflection and Refraction

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Tathagata Basak: A monstrous(?) complex hyperbolic orbifold

I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster

From playlist Topology

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Group theory 13: Dihedral groups

This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.

From playlist Group theory

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Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Geometry and arithmetic of sphere packings - Alex Kontorovich

Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Related pages

Affine group | Lie group | ADE classification | Finite field | Point groups in two dimensions | Platonic solid | Chevalley–Shephard–Todd theorem | Isometry group | Discrete group | Frieze group | General linear group | Tessellation | Cartan–Dieudonné theorem | Regular polytope | Hyperbolic space | Shear mapping | Rotation | Symmetry group | Dihedral group | Point groups in three dimensions | Wallpaper group | Coxeter group | Field (mathematics) | Weyl group | Riemannian manifold | Group theory | Euclidean space | N-sphere | Complex reflection group | Orthogonal group | Fundamental domain | Triangle group | Geometry | Reflection (mathematics)