Year: 2026
Type: article
Abstract: A braid representation is a monoidal functor from the braid category $${\mathsf B}$$ B , for example given by a solution to the constant Yang-Baxter equation. Given a monoidal category $$\textsf{C}$$ C with $$ob(\textsf{C})={\mathbb N}$$ o b ( C ) = N , a rank- N charge-conserving representation, or spin-chain representation, is a strict monoidal functor F from $$\textsf{C}$$ C to the category $${\textsf{Match}}^N$$ Match N of rank- N charge-conserving matrices (see below for definition), that is natural in the sense that $$F(1)=1$$ F ( 1 ) = 1 . In this work we construct all spin-chain braid representations, and classify up to suitable notions of isomorphism.
Authors: Paul Martin, Eric C. Rowell
Institutions: University of Leeds, Texas A&M University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4226216008