Representations of flat virtual braids which do not preserve the forbidden relations Научная публикация
| Журнал |
Journal of Knot Theory and its Ramifications
ISSN: 0218-2165 |
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| Вых. Данные | Год: 2023, Том: 32, Номер: 4, Номер статьи : 2350093, Страниц : 27 DOI: 10.1142/S0218216523500931 | ||||||||
| Ключевые слова | Flat virtual braids, braid-like groups, representations by automorphisms | ||||||||
| Авторы |
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| Организации |
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Информация о финансировании (3)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0002 |
| 2 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0009 |
| 3 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0004 |
Реферат:
In the paper, we construct a representation theta:FVB_n→{\rm Aut}(F_{2n})$ of the flat virtual braid group FVB_n on n strands by automorphisms of the free group F_{2n} with 2n generators which does not preserve the forbidden relations in the flat virtual braid group. This representation gives a positive answer to the problem formulated by V. Bardakov in the list of unsolved problems in virtual knot theory and combinatorial knot theory by R. Fenn, D. Ilyutko, L. Kauffman and V. Manturov. Using this representation we construct a new group invariant for flat welded links. Also we find the set of normal generators of the groups VP_n\cap H_n in VB_n, FVP_n\cap FH_n in FVB_n, GVP_n\cap GH_n in GVB_n, which play an important role in the study of the kernel of the representation theta.
Библиографическая ссылка:
Bardakov V.
, Chuzhinov B.
, Emel'yanenkov I.
, Ivanov M.
, Markhinina E.
, Nasybullov T.
, Panov S.
, Singh N.
, Vasyutkin S.
, Yakhin V.
, Vesnin A.
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Representations of flat virtual braids which do not preserve the forbidden relations
Journal of Knot Theory and its Ramifications. 2023. V.32. N4. 2350093 :1-27. DOI: 10.1142/S0218216523500931 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 7 окт. 2020 г. |
| Принята к публикации: | 20 сент. 2023 г. |
| Опубликована в печати: | 25 нояб. 2023 г. |
| Опубликована online: | 27 февр. 2024 г. |
Идентификаторы БД:
| Web of science: | WOS:001183905800005 |
| Scopus: | 2-s2.0-85186938742 |
| РИНЦ: | 65181941 |
| OpenAlex: | W3092523305 |