The centralizer of a Coxeter element
Ruwen Hollenbach, Patrick Wegener
TL;DR
This paper proves that in an irreducible Coxeter group, the centralizer of a Coxeter element is exactly the cyclic group generated by that element, clarifying the structure of such centralizers.
Contribution
It establishes that the centralizer of a Coxeter element in an irreducible Coxeter group is cyclic, providing a precise structural characterization.
Findings
The centralizer of a Coxeter element is cyclic.
The centralizer equals the subgroup generated by the Coxeter element.
This result applies to all irreducible Coxeter groups.
Abstract
We prove that the centralizer of a Coxeter element in an irreducible Coxeter group is the cyclic group generated by that Coxeter element.
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Taxonomy
TopicsSupramolecular Self-Assembly in Materials · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models