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Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature

Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

Authors

Gwendolyn E. Barnes

Richard J. Szabo



Abstract

We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.

Citation

Barnes, G. E., Schenkel, A., & Szabo, R. J. (2016). Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature. Journal of Geometry and Physics, 106, 234-255. https://doi.org/10.1016/j.geomphys.2016.04.005

Journal Article Type Article
Acceptance Date Apr 4, 2016
Online Publication Date Apr 19, 2016
Publication Date 2016-08
Deposit Date Mar 2, 2017
Publicly Available Date Mar 2, 2017
Journal Journal of Geometry and Physics
Print ISSN 0393-0440
Electronic ISSN 0393-0440
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 106
Pages 234-255
DOI https://doi.org/10.1016/j.geomphys.2016.04.005
Keywords Noncommutative/nonassociative differential geometry; Quasi-Hopf algebras; Braided monoidal categories; Internal homomorphisms; Cochain twist quantization
Public URL http://eprints.nottingham.ac.uk/id/eprint/41003
Publisher URL https://doi.org/10.1016/j.geomphys.2016.04.005
Related Public URLs https://arxiv.org/abs/1507.02792
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0
Additional Information This article is maintained by: Elsevier; Article Title: Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature; Journal Title: Journal of Geometry and Physics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.geomphys.2016.04.005; Content Type: article; Copyright: © 2016 Elsevier B.V. All rights reserved.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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