Multi-virtual braid groups
Abstract
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index . We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. Also, we introduce multi-welded and multi-unrestricted braid groups and examines structure of three-strand 2-virtual braid group and some its subgroups and quotients. The paper concludes by outlining open problems and suggesting avenues for future research in this area.
Keywords
Cite
@article{arxiv.2507.14551,
title = {Multi-virtual braid groups},
author = {Valeriy G. Bardakov and Tatyana A. Kozlovskaya and Komal Negi and Madeti Prabhakar},
journal= {arXiv preprint arXiv:2507.14551},
year = {2026}
}
Comments
23 pages, 12 figures