Noncommutative Manifolds, the Instanton Algebra and Isospectral Deformations
Alain Connes,Giovanni Landi +1 more
TLDR
In this paper, the authors give new examples of non-commutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn.Abstract:
We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features.read more
Citations
More filters
Journal ArticleDOI
Noncommutative geometry and gravity
Paolo Aschieri,Marija Dimitrijevic,Marija Dimitrijevic,Marija Dimitrijevic,Frank Meyer,Frank Meyer,Julius Wess,Julius Wess +7 more
TL;DR: In this article, a deformation of infinitesimal diffeomorphisms of a smooth manifold is studied and a differential geometry on a noncommutative algebra of functions whose product is a star product is developed.
Journal ArticleDOI
Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples
TL;DR: In this paper, a 3-parameter family of deformations of the standard 3-sphere S3 and a corresponding 3parameter deformation of the 4-dimensional Euclidean space ℝ4u are studied.
Journal ArticleDOI
Moyal Planes are Spectral Triples
Victor Gayral,Victor Gayral,José M. Gracia-Bondía,Bruno Iochum,Bruno Iochum,Thomas Schucker,Thomas Schucker,Joseph C. Várilly,Joseph C. Várilly +8 more
TL;DR: Axioms for non-unital spectral triples, extending those introduced in the unital case by Connes, are proposed in this paper, and for the sake of their importance in noncommutative quantum field theory, the spaces R2N endowed with Moyal products are intensively investigated.
Book
An Introduction to Noncommutative Geometry
TL;DR: In this paper, a course on non-commutative geometry from the non-computative point of view was presented at the 1997 Summer School on Non-Commutative Geometry and Applications at the European Mathematical Society (EMS) at Monsaraz and Lisboa, Portugal, September 1-10, 1997.
Book ChapterDOI
Supporting frequent updates in R-trees: a bottom-up approach
TL;DR: In this article, a bottom-up update strategy for R-trees is proposed to improve the performance of R-tree updates by using a compact main-memory summary structure that allows direct access to the index nodes.
References
More filters
Journal ArticleDOI
String theory and noncommutative geometry
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this article, a non-zero B-field is introduced for string theory and the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and the corrections away from this limit are discussed.
Journal ArticleDOI
Noncommutative Geometry and Matrix Theory: Compactification on Tori
Alain Connes,Michael R. Douglas,Michael R. Douglas,Albert Schwarz,Albert Schwarz,Albert Schwarz +5 more
TL;DR: In this paper, the authors studied toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry, and argued that they correspond in supergravity to tori with constant background three-form tensor field.
Journal ArticleDOI
Gravity coupled with matter and the foundation of non-commutative geometry
TL;DR: In this article, simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds were shown to give the SM Lagrangian coupled to gravity.
Journal ArticleDOI
Twisted SU (2) group. An example of a non-commutative differential calculus
TL;DR: In this paper, a C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν is presented.
Book
Elements of Noncommutative Geometry
TL;DR: In this article, a wide range of topics including sources of non-commutative geometry, fundamentals of Non-Commutative topology, K-theory and Morita equivalance, non-commodity integrodifferential calculus, noncommutativity Riemannian spin manifolds, commutative geometrics, tori, second quantization, quantum field theory, and pseudodifferential operators are discussed.