2015/07/31 by Gwendolyn E. Barnes, Alexander Schenkel, Richard J. Szabo · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Black Holes and Theoretical Physics #Category theory #Cellular algebra #Collineation #Differential (mechanical device) #Differential algebraic geometry #Differential equation #Differential form #Differential geometry #Homomorphism #Hopf algebra #Hopf fibration #Mathematical analysis #Mathematics #Morphism #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Projective differential geometry #Projective space #Projective test #Pure mathematics #Quantum differential calculus #Quasitriangular Hopf algebra #hep-th #math-ph #math.CT #math.MP #math.QA #msc:16T05 #msc:17B37 #msc:46L87 #msc:53D55
paper · pdf · doi:10.1016/j.geomphys.2016.04.005
published as Journal of Geometry and Physics, Volume 106, August 2016, Pages 234-255 · 29 pages. v2: Final version published in Journal of Geometry and Physics
openalex publication_date 2016/04/30 · arxiv created 2016/05/02 · arxiv updated 2016/05/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.