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

Gwendolyn Elizabeth Barnes, Alexander Schenkel, Richard Joseph Szabo

Research output: Contribution to journalArticle

13 Citations (Scopus)
17 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)234–255
Number of pages22
JournalJournal of Geometry and Physics
Volume106
Early online date19 Apr 2016
DOIs
Publication statusPublished - Aug 2016

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