Centralizers of parabolic subgroups of Artin groups of type \(A_l\), \(B_l\), and \(D_l\) (Q1372633)
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scientific article; zbMATH DE number 1088590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Centralizers of parabolic subgroups of Artin groups of type \(A_l\), \(B_l\), and \(D_l\) |
scientific article; zbMATH DE number 1088590 |
Statements
Centralizers of parabolic subgroups of Artin groups of type \(A_l\), \(B_l\), and \(D_l\) (English)
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12 March 2000
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Let \((A,\Sigma)\) be a Coxeter system and let \(X\subseteq\Sigma\). The subgroup \(A_X\) of \(A\) generated by \(X\) is called a parabolic subgroup. The author finds a generating set for the centralizer of \(A_X\) in \(A\) in case (i) the Coxeter graph of \(A_X\) is connected (i.e., \(A_X\) is not a nontrivial direct product) and (ii) \(A\) has one of the types \(A_n\), \(B_n\) or \(D_n\).
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Artin groups
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parabolic subgroups
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Coxeter systems
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generating sets
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centralizers
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