# Virtual and universal braid groups, their quotients and representations

@inproceedings{Bardakov2021VirtualAU, title={Virtual and universal braid groups, their quotients and representations}, author={Valerij G. Bardakov and I. Emel'yanenkov and Maxim Ivanov and T. A. Kozlovskaya and Timur Nasybullov and A. Vesnin}, year={2021} }

In the present paper we study structural aspects of certain quotients of braid groups and virtual braid groups. In particular, we construct and study linear representations Bn → GLn(n−1)/2 ( Z[t] ) , V Bn → GLn(n−1)/2 ( Z[t, t 1 , t ±1 2 , . . . , t ±1 n−1] ) which are connected with the famous Lawrence-Bigelow-Krammer representation. It turns out that these representations are faithful representations of crystallographic groups Bn/P ′ n, V Bn/V P ′ n, respectively. Using these representations… Expand

#### One Citation

Virtual braid groups, virtual twin groups and crystallographic groups

- Mathematics
- 2021

Let n ≥ 2. Let V Bn (resp. V Pn) be the virtual braid group (resp. the pure virtual braid group), and let V Tn (resp. PV Tn) be the virtual twin group (resp. the pure virtual twin group). Let Π be… Expand

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