On the first order operators in bimodules

Abstract

We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.

13 pages, AMSLaTeX

References in corpus (3)

• Linear Connections in Non-Commutative Geometry
• Linear connections on the quantum plane
• Linear connections on matrix geometries

Cited by in corpus (20)

• Quantum Space-time and Classical Gravity
• Exceptional quantum geometry and particle physics
• Gravity induced from quantum spacetime
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Differential Calculus on Fuzzy Sphere and Scalar Field
• Holomorphic structures on the quantum projective line
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
• Quantum gravity on a square graph
• Almost commutative Riemannian geometry: wave operators
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Noncommutative principal bundles through twist deformation
• Non-commutative geometry and the standard model vacuum
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• Connes-Lott model building on the two-sphere
• Twisting all the way: from algebras to morphisms and connections
• Quantum Koszul formula on quantum spacetime
• Connections over twisted tensor products of algebras
• Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds
• Deformation quantization of principal bundles
• Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids