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

Barnes, Gwendolyn E. and Schenkel, Alexander and Szabo, Richard J. (2016) Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature. Journal of Geometry and Physics, 106 . pp. 234-255. ISSN 0393-0440

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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.

Item Type: Article
Keywords: Noncommutative/nonassociative differential geometry; Quasi-Hopf algebras; Braided monoidal categories; Internal homomorphisms; Cochain twist quantization
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
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Depositing User: Schenkel, Dr Alexander
Date Deposited: 02 Mar 2017 15:05
Last Modified: 04 May 2020 18:04

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