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Concept
Coxeter Groups
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Summary
Coxeter Groups
are
Abstract groups
that can be represented by
Reflections across hyperplanes
in a
Euclidean Space
, and they play a fundamental role in the
Study of symmetries
and
Geometric Structures
. They are defined by a
Set of generators
subject to relations that can be encoded in a
Coxeter Matrix
or diagram, allowing for the classification and
Analysis of symmetrical properties
in
Various dimensions
.
Concepts
Reflection Group
Coxeter Matrix
Coxeter Diagram
Weyl Group
Root System
Simple Reflection
Geometric Group Theory
Hyperplane Arrangement
Affine Coxeter Group
Spherical Coxeter Group
Bruhat Order
Tits Cone
Dynkin Diagram
Artin Groups
Hyperplane Arrangements
Relevant Degrees
Algebra 67%
Geometry 33%
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