On Curvature in Noncommutative Geometry

Abstract

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra. The corresponding curvatures are also compared.

16 pages, PlainTex

References in corpus (10)

• Gravity in Non-Commutative Geometry
• Connections on central bimodules
• Linear Connections in Non-Commutative Geometry
• Noncommutative Geometry of Finite Groups
• Linear connections on the quantum plane
• Gravity and Electromagnetism in Noncommutative Geometry
• Linear connections on matrix geometries
• Gravity from Noncommutative Geometry
• Grading of Spinor Bundles and Gravitating Matter in Non-Commutative Geometry
• On The non-commutative Riemannian geometry of GL_q(n)

Cited by in corpus (41)

• Quantum Space-time and Classical Gravity
• Cellular Networks as Models for Planck-Scale Physics
• Spherically Symmetric Noncommutative Space: d = 4
• Riemannian Geometry of Noncommutative Surfaces
• Can noncommutativity resolve the Big-Bang singularity?
• Finite Field Theory on Noncommutative Geometries
• Noncommutative Geometry of the h-deformed Quantum Plane
• Teleparallel Equivalent of the Kaluza-Klein Theory
• Gravity on Fuzzy Space-Time
• The Geometry of a $q$-Deformed Phase Space
• On the Gauss-Chern-Bonnet theorem for the noncommutative 4-sphere
• The Geometry of the Quantum Euclidean Space
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• A Dynamical 2-dimensional Fuzzy Space
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• Riemannian Geometry of a Discretized Circle and Torus
• n=3 Nilpotent differential calculus on some non-commutative (super) spaces
• Lectures on Differential Geometry of Modules and Rings
• Noncommutative 2-Dimensional Models of Gravity
• Levi-Civita connections on quantum spheres
• Twisted submanifolds of R^n
• Non Commutative Differential Geometry, and the Matrix Representations of Generalised Algebras
• Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
• Classical Gravity on Fuzzy Space-Time
• Linear Connections on Graphs
• Connes Trace Theorem for Curved Noncommutative Tori. Application to Scalar Curvature
• Fuzzy Surfaces of Genus Zero
• Noncommutative geometry of phase space
• Hochschild DGLAs and torsion algebras
• On q-deformed Levi-Civita connections
• A note on Connections and Bimodules
• Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model',12. - 17. July 2003, Portoroz, Slovenia (Part 2 of 2)
• A noncommutative geometric approach to the quantum structure of spacetime
• Geometrical techniques for the N-dimensional Quantum Euclidean Spaces
• A noncommutative catenoid
• Non-commutative connections of the second kind
• Frame formalism for the N-dimensional quantum Euclidean spaces
• Fuzzy Space-Time
• Metrics on the Real Quantum Plane
• Jets and connections in commutative and noncommutative geometry