Аннотация

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 ]) B_{n}\to\mathrm{GL}_{n(n-1)/2}(\mathbb{Z}[t^{\pm 1}]), VB n → GL n (n - 1) / 2 (Z [ t ± 1, t 1 ± 1, t 2 ± 1, ..., t n - 1 ± 1 ]) \mathrm{VB}_{n}\to\mathrm{GL}_{n(n-1)/2}(\mathbb{Z}[t^{\pm 1},t_{1}^{\pm 1},t_{2}^{\pm 1},\ldots,t_{n-1}^{\pm 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 ′ B_{n}/P_{n}^{\prime}, VB n / VP n ′ \mathrm{VB}_{n}/\mathrm{VP}_{n}^{\prime}, respectively. Using these representations we study certain properties of the groups B n / P n ′ B_{n}/P_{n}^{\prime}, VB n / VP n ′ \mathrm{VB}_{n}/\mathrm{VP}_{n}^{\prime}. Moreover, we construct new representations and decompositions of the universal braid groups UB n \mathrm{UB}_{n}.

Язык оригиналаанглийский
Страницы (с-по)679-712
Число страниц34
ЖурналJournal of Group Theory
Том25
Номер выпуска4
DOI
СостояниеОпубликовано - 1 июл. 2022

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Подробные сведения о темах исследования «Virtual and universal braid groups, their quotients and representations». Вместе они формируют уникальный семантический отпечаток (fingerprint).

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