Reflection groups | Coxeter groups

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example. However, not all Coxeter groups are finite, and not all can be described in terms of symmetries and Euclidean reflections. Coxeter groups were introduced in 1934 as abstractions of reflection groups, and finite Coxeter groups were classified in 1935. Coxeter groups find applications in many areas of mathematics. Examples of finite Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter groups include the triangle groups corresponding to regular tessellations of the Euclidean plane and the hyperbolic plane, and the Weyl groups of infinite-dimensional Kac–Moody algebras. Standard references include and. (Wikipedia).

Olga Varghese: Automorphism groups of Coxeter groups do not have Kazhdan's property (T)

CIRM VIRTUAL EVENT Recorded during the meeting "Virtual Geometric Group Theory conference " the May 27, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIR

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Group theory 23: Coxeter Todd algorithm

This lecture is part of an online mathematics course on group theory. It describes the Coxeter-Todd algorithm for coset enumeration, and gives some examples of it.

From playlist Group theory

Hankyung Ko: A singular Coxeter presentation

SMRI Algebra and Geometry Online Hankyung Ko (Uppsala University) Abstract: A Coxeter system is a presentation of a group by generators and a specific form of relations, namely the braid relations and the reflection relations. The Coxeter presentation leads to, among others, a similar pre

From playlist SMRI Algebra and Geometry Online

Cong He: Right-angled Coxeter Groups with Menger Curve Boundary

Cong He, University of Wisconsin Milwaukee Title: Right-angled Coxeter Groups with Menger Curve Boundary Hyperbolic Coxeter groups with Sierpinski carpet boundary was investigated by {\'S}wi{\c{a}}tkowski. And hyperbolic right-angled Coxeter group with Gromov boundary as Menger curve was s

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Abstract Algebra | Cyclic Subgroups

We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

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Jacob goes into detail on some particularly important finite groups, and explains how groups and subgroups can be generated by their elements, along with some important consequences.

From playlist Basics: Group Theory

Group Theory: The Center of a Group G is a Subgroup of G Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof

From playlist Abstract Algebra

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

Invariants of Graphs, Their Associated Clique Complexes and Right-Angled... - Michael Davis

Michael Davis The Ohio State University; Member, School of Mathematics October 19, 2010 Associated to any simplicial graph there is a right-angled Coxeter group. Invariants of the Coxeter group such as its growth series or its weighted L^2 Betti numbers can be computed from the graph's cli

From playlist Mathematics

From Coxeter Higher-Spin Theories to Strings and Tensor Models by Mikhail Vasiliev

ORGANIZERS : Pallab Basu, Avinash Dhar, Rajesh Gopakumar, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, Suvrat Raju, Sandip Trivedi and Spenta Wadia DATE : 21 May 2018 to 02 June 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore In the past twenty years, the discovery of the AdS/C

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Homological Algebra(Homo Alg) 5 by Graham Ellis

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Cyclic Groups (Abstract Algebra)

Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s

From playlist Abstract Algebra

Vic Reiner, Lecture III - 13 February 2015 (49)

Vic Reiner (University of Minnesota) - Lecture III 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 question

From playlist Vertex algebras, W-algebras, and applications - 2014-2015

Osamu Iyama: Preprojective algebras and Cluster categories

Abstract: The preprojective algebra P of a quiver Q has a family of ideals Iw parametrized by elements w in the Coxeter group W. For the factor algebra Pw=P/Iw, I will discuss tilting and cluster tilting theory for Cohen-Macaulay Pw-modules following works by Buan-I-Reiten-Scott, Amiot-Rei

From playlist Combinatorics

Geometry and arithmetic of sphere packings - Alex Kontorovich

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From playlist Mathematics

Diophantine analysis in thin orbits - Alex Kontorovich

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Visual Group Theory, Lecture 2.1: Cyclic and abelian groups

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From playlist Visual Group Theory