Blocked-braid Groups

Abstract

We introduce and study a family of groups ${\mathbf{BB}}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups ${\mathbf{B}}_n$, and have the corresponding symmetric groups ${\Sigma }_n$ as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in ${\mathbf{BB}}_n$ is Dirac's Belt Trick; that torsion through $4\pi$ is equal to the identity. We show that ${\mathbf{BB}}_n$ is finite for $n=1,2$ and 3 but infinite for $n>3$.

References in corpus (1)

• Cospans and spans of graphs: a categorical algebra for the sequential and parallel composition of discrete systems