Algebraic structures among virtual singular braids

Abstract

We show that the virtual singular braid monoid on $n$ strands embeds in a group $VS{G}_n$, which we call the virtual singular braid group on $n$ strands. The group $VS{G}_n$ contains a normal subgroup $VSP{G}_n$ of virtual singular pure braids. We show that $VS{G}_n$ is a semi-direct product of $VSP{G}_n$ and the symmetric group $S_n$. We provide a presentation for $VSP{G}_n$ via generators and relations. We also represent $VSP{G}_n$ as a semi-direct product of $n-1$ subgroups and study the structures of these subgroups. These results yield a normal form of words in the virtual singular braid group.

20 pages, 2 figures

References in corpus (2)

• Virtual singular braids and links
• On the virtual singular braid monoid