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- Title
Virtual and universal braid groups, their quotients and representations.
- Authors
Bardakov, Valeriy; Emel'yanenkov, Ivan; Ivanov, Maxim; Kozlovskaya, Tatyana; Nasybullov, Timur; Vesnin, Andrei
- Abstract
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 B n → GL n (n - 1) / 2 (Z [ t ± 1 ]) , VB n → GL n (n - 1) / 2 (Z [ t ± 1 , t 1 ± 1 , t 2 ± 1 , ... , t n - 1 ± 1 ]) which are connected with the famous Lawrence–Bigelow–Krammer representation. It turns out that these representations induce faithful representations of the crystallographic groups B n / P n ′ , VB n / VP n ′ , respectively. Using these representations we study certain properties of the groups B n / P n ′ , VB n / VP n ′ . Moreover, we construct new representations and decompositions of the universal braid groups UB n .
- Subjects
GROUPOIDS
- Publication
Journal of Group Theory, 2022, Vol 25, Issue 4, p679
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2021-0114