Martin, P. orcid.org/0000-0002-8141-9465 and Rowell, E.C. (2026) Classification of Spin-Chain Braid Representations. Communications in Mathematical Physics, 407 (10). 201. ISSN: 0010-3616
Abstract
A braid representation is a monoidal functor from the braid category B, for example given by a solution to the constant Yang-Baxter equation. Given a monoidal category C with ob(C) = N, a rank-N charge-conserving representation, or spin-chain representation, is a strict monoidal functor F from C to the category Matchᴺ of rank-N charge-conserving matrices (see below for definition), 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.
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| Copyright, Publisher and Additional Information: | © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
| Funding Information: | Funder Grant number EPSRC Accounts Payable EP/W007509/1 |
| Date Deposited: | 24 Aug 2026 14:16 |
| Last Modified: | 07 Oct 2026 15:37 |
| Status: | Published |
| Publisher: | Springer Nature |
| Identification Number: | 10.1007/s00220-026-05716-z |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:244628 |
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