In mathematics, a Coxeter element is an element of an irreducible Coxeter group formed as a product of all of the group's simple reflections; the specific element produced depends on the order in which the reflections are multiplied, but every such ordering yields conjugate elements sharing the same order, called the Coxeter number of the group. Coxeter elements are named after the British-Canadian geometer H. S. M. Coxeter, who introduced Coxeter groups in 1934 as an abstraction of reflection groups.
Facts
Origin YearCoxeter introduced the groups in 1934 as abstractions of reflection groups Classification
Object KindStructure or Algebraic Object 1 Connections
Attributed To
Source Coxeter Element (Wikipedia)
In Branch
Source Wolfram MathWorld: Coxeter Element
Is Kind Of Object
Principal Result Of
Source Coxeter Element (Wikipedia)
Sources
1. Coxeter Element (Wikipedia)
Lead section
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections.
Attributed To: Harold Scott MacDonald Coxeter, Lead sentence
Coxeter, who introduced the groups in 1934 as abstractions of reflection groups.
Principal Result Of: Harold Scott MacDonald Coxeter, Lead sentence of the article on the result
Coxeter, who introduced the groups in 1934 as abstractions of reflection groups.
View the SourceWolfram MathWorld: Coxeter Element
Wolfram MathWorldIn Branch: Group Theory, Subject classificationsQuote, In Branch: Group Theory, Subject classifications
Algebra Group Theory
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