Cirio, LS and Faria Martins, J orcid.org/0000-0001-8113-3646 (2012) Categorifying the Knizhnik–Zamolodchikov connection. Differential Geometry and its Applications, 30 (3). pp. 238-261. ISSN 0926-2245
Abstract
In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of n particles in the complex plane, categorifying the Knizhnik–Zamolodchikov connection. To this end, we define the differential crossed module of horizontal 2-chord diagrams, categorifying the Lie algebra of horizontal chord diagrams in a set of n parallel copies of the interval. This therefore yields a categorification of the 4-term relation. We carefully discuss the representation theory of differential crossed modules in chain-complexes of vector spaces, which makes it possible to formulate the notion of an infinitesimal 2-R matrix in a differential crossed module.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012 Elsevier B.V. This is an author produced version of a paper published in Differential Geometry and its Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Higher gauge theory Braided surface Two-dimensional holonomy Chord diagrams Infinitesimal braiding 4-term relation Differential crossed module Knizhnik–Zamolodchikov equations Categorical representation |
Dates: |
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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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Sep 2017 13:39 |
Last Modified: | 24 Feb 2018 17:36 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.difgeo.2012.03.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112771 |