Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature
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 constru...
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41003/ |
| _version_ | 1848796175754330112 |
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| author | Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J. |
| author_facet | Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J. |
| author_sort | Barnes, Gwendolyn E. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:49Z |
| format | Article |
| id | nottingham-41003 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:49Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410032020-05-04T18:04:56Z https://eprints.nottingham.ac.uk/41003/ Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J. 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. Elsevier 2016-08-31 Article PeerReviewed Barnes, Gwendolyn E., 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 Noncommutative/nonassociative differential geometry; Quasi-Hopf algebras; Braided monoidal categories; Internal homomorphisms; Cochain twist quantization https://doi.org/10.1016/j.geomphys.2016.04.005 doi:10.1016/j.geomphys.2016.04.005 doi:10.1016/j.geomphys.2016.04.005 |
| spellingShingle | Noncommutative/nonassociative differential geometry; Quasi-Hopf algebras; Braided monoidal categories; Internal homomorphisms; Cochain twist quantization Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J. Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title | Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title_full | Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title_fullStr | Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title_full_unstemmed | Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title_short | Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature |
| title_sort | nonassociative geometry in quasi-hopf representation categories ii: connections and curvature |
| topic | Noncommutative/nonassociative differential geometry; Quasi-Hopf algebras; Braided monoidal categories; Internal homomorphisms; Cochain twist quantization |
| url | https://eprints.nottingham.ac.uk/41003/ https://eprints.nottingham.ac.uk/41003/ https://eprints.nottingham.ac.uk/41003/ |