Abstract:
We study a representation of the virtual braid group VBn into the automorphism group of a free product of a free group and a free Abelian group, proposed by S. Kamada. It is proved that the given representation is equivalent to the representation constructed in [http://arxiv.org/abs/1603.01425]; i.e. the kernels of these representations coincide.
Citation:
V. G. Bardakov, M. V. Neshchadim, “A representation of virtual braids by automorphisms”, Algebra Logika, 56:5 (2017), 539–547; Algebra and Logic, 56:5 (2017), 355–361
This publication is cited in the following 9 articles:
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, “Singular braids, singular links and subgroups of camomile type”, Topology and its Applications, 2025, 109206
V. G. Bardakov, B. B. Chuzhinov, I. A. Emelyanenkov, M. E. Ivanov, T. A. Kozlovskaya, V. E. Leshkov, “Set-Theoretical Solutions of the n-Simplex Equation”, Sib. Adv. Math., 34:1 (2024), 1
Valeriy Bardakov, Timur Nasybullov, “Multi-switches and representations of braid groups”, J. Algebra Appl., 23:03 (2024)
Valeriy Bardakov, Bogdan Chuzhinov, Ivan Emel'yanenkov, Maxim Ivanov, Elizaveta Markhinina, Timur Nasybullov, Sergey Panov, Nina Singh, Sergey Vasyutkin, Valeriy Yakhin, Andrei Vesnin, “Representations of flat virtual braids which do not preserve the forbidden relations”, J. Knot Theory Ramifications, 32:14 (2023)
Bardakov V.G., Neshchadim V M., Singh M., “Virtually Symmetric Representations and Marked Gauss Diagrams”, Topology Appl., 306 (2022), 107936
Valeriy Bardakov, Ivan Emel'yanenkov, Maxim Ivanov, Tatyana Kozlovskaya, Timur Nasybullov, Andrei Vesnin, “Virtual and universal braid groups, their quotients and representations”, Journal of Group Theory, 2022
V. Bardakov, T. Nasybullov, “Multi-switches and virtual knot invariants”, Topology Appl., 293 (2021), 107552
D A Baev, L V Cherckesova, O A Safaryan, V O Kravchenko, P V Razumov, “Modification of Anshel-Anshel-Goldfeld Postquantum Algorithm / Protocol Based on Algebraic Braid Groups, in Order to the Span–Cyberattack Neutralization”, J. Phys.: Conf. Ser., 2131:2 (2021), 022079
V. G. Bardakov, T. R. Nasybullov, “Multi-switches, representations of virtual braids, and invariants of virtual links”, Algebra and Logic, 59:4 (2020), 341–345