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Concept
Coxeter Group
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Summary
A
Coxeter Group
is an
Abstract Group
defined by a
Set of generators
subject to
Specific relations
, primarily involving
Products of pairs
of generators that are involutions. These groups are fundamental in the
Study of symmetries
and have applications in various fields, including geometry, algebra, and combinatorics.
Concepts
Abstract Group
Generators And Relations
Involutions
Symmetry
Reflection Group
Weyl Group
Root System
Coxeter-Dynkin Diagram
Geometric Representation
Tits Cone
Bruhat Order
Dynkin Diagrams
Affine Coxeter Group
Coxeter Diagram
Coxeter Matrix
Regular Polytopes
Tits System
Cartan Matrix
Relevant Degrees
Algebra 70%
Geometry 30%
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