Linear representation of cactus groups | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2025. № 96. DOI: 10.17223/19988621/96/1

Linear representation of cactus groups

The cactus group Jn, n > 2, can be generated by n - 1 elements. In this paper, using the representation in these generators, we construct a linear representation of the cactus group. We prove that the image of the resulting representation is isomorphic to the permutation group Sn and that for all n > 3, this representation is not faithful.

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Keywords

cactus group, symmetric group, presentation by generators and relations, linear representation, faithful representation

Authors

Name	Organization	E-mail
Zimireva Ksenia V.	Novosibirsk State University	k.zimireva@g.nsu.ru

Всего: 1

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