Classification of spin-chain braid representations Institutional Repository Document uri icon


  • A braid representation is a monoidal functor from the braid category $mathsf{B}$, for example given by a solution to the constant Yang-Baxter equation. Given a monoidal category $mathsf{C}$ with $ob(mathsf{C})=mathbb{N}$, a rank-$N$ charge-conserving representation (or spin-chain representation) is a strict monoidal functor $F$ from $mathsf{C}$ to the category $mathrm{Match}^N$ of rank-$N$ charge-conserving matrices that is natural in the sense that $F(1)=1$}. In this work we construct all spin-chain braid representations, and classify up to suitable notions of isomorphism.

author list (cited authors)

  • Martin, P., & Rowell, E. C.

complete list of authors

  • Martin, Paul||Rowell, Eric C

publication date

  • December 2021