Linearity of generalized cactus groups

Cactus groups are traditionally defined based on symmetric groups, and pure cactus groups are particular subgroups of cactus groups. Mostovoy [6] showed that pure cactus groups embed into right-angled Coxeter groups. We generalize this result to cactus groups associated with arbitrary finite Coxeter...

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Bibliographic Details
Published in:Journal of algebra 2023-12, Vol.635, p.256-270
Main Author: Yu, Runze
Format: Article
Language:English
Subjects:
Coxeter group
Generalized cactus group
Generalized pure cactus group
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Summary:Cactus groups are traditionally defined based on symmetric groups, and pure cactus groups are particular subgroups of cactus groups. Mostovoy [6] showed that pure cactus groups embed into right-angled Coxeter groups. We generalize this result to cactus groups associated with arbitrary finite Coxeter groups and we investigate some representations of generalized cactus groups and deduce the linearity of generalized cactus groups.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2023.07.039