Local representations of the loop braid group

Abstract

We study representations of the loop braid group $LB_n$ from the perspective of extending representations of the braid group $B_n$. We also pursue a generalization of the braid/Hecke/Temperlely-Lieb paradigm---uniform finite dimensional quotient algebras of the loop braid group algebras.

22 pages, 1 figure. Revised introduction and title. Add a reference and fix minor typos