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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Main Authors:	Barnes, Gwendolyn E., Schenkel, Alexander, Szabo, Richard J.
Format:	Article
Language:	English
Published:	Elsevier 2016
Online Access:	http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/1/NAG2.pdf

id	nottingham-41003
recordtype	eprints
spelling	nottingham-410032018-06-27T09:35:34Z http://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 application/pdf en cc_by_nc_nd http://eprints.nottingham.ac.uk/41003/1/NAG2.pdf 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 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
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
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.
format	Article
author	Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J.
spellingShingle	Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J. Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature
author_facet	Barnes, Gwendolyn E. Schenkel, Alexander Szabo, Richard J.
author_sort	Barnes, Gwendolyn E.
title	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_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_sort	nonassociative geometry in quasi-hopf representation categories ii: connections and curvature
publisher	Elsevier
publishDate	2016
url	http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/ http://eprints.nottingham.ac.uk/41003/1/NAG2.pdf
first_indexed	2018-09-06T13:10:04Z
last_indexed	2018-09-06T13:10:04Z
_version_	1610863769809846272

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

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