论文标题
虚拟奇异辫子之间的代数结构
Algebraic structures among virtual singular braids
论文作者
论文摘要
我们表明，$ n $ strands嵌入$ vsg_n $上的虚拟单数辫子单片，我们称之为$ n $ strands上的虚拟单数编织组。组$ vsg_n $包含一个普通的子组$ vspg_n $的虚拟单数纯辫子。我们证明$ vsg_n $是$ vspg_n $的半独联产品和对称组$ s_n $。我们通过生成器和关系为$ vspg_n $提供了演示文稿。我们还代表$ vspg_n $作为$ n-1 $子组的半主导产品，并研究了这些子组的结构。这些结果在虚拟单数编织组中产生正常的单词形式。
We show that the virtual singular braid monoid on $n$ strands embeds in a group $VSG_n$, which we call the virtual singular braid group on $n$ strands. The group $VSG_n$ contains a normal subgroup $VSPG_n$ of virtual singular pure braids. We show that $VSG_n$ is a semi-direct product of $VSPG_n$ and the symmetric group $S_n$. We provide a presentation for $VSPG_n$ via generators and relations. We also represent $VSPG_n$ 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.
