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

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

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: https://nottingham-repository.worktribe.com/output/803525
• Publisher URL: https://doi.org/10.1016/j.geomphys.2016.04.005
• Related Public URLs: https://arxiv.org/abs/1507.02792
• 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.