Linearity of Generalized Cactus Groups

2022/02/02 by Runze Yu, Yu, Runze
Engineering · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2202.00860

openalex publication_date 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cactus groups are traditionally defined based on symmetric groups, and pure cactus groups are particular subgroups of cactus groups. Mostovoy 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.

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• Cactus groups from the viewpoint of geometric group theory
• Cactus groups, twin groups, and right-angled Artin groups
• Combinatorics of affine cactus groups
• Cactus groups and Lusztig's asymptotic algebra
• Minimal generating set of cactus groups