Noncommutative Geometry

  title={Noncommutative Geometry},
  author={Andrew S. Lesniewski},
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In particular, this observation proved to be extremely fruitful in algebraic geometry and has led to tremendous progress in this subject over the past few decades. In these developments the concept of a point in a space is secondary and overshadowed by the algebraic properties of the (sheaves of) rings of… 

Cyclic cohomology and the noncommutative Chern character

Noncommutative Geometry is an area of mathematics which has been dominated by the work of Alain Connes in the last 20-25 years. The basic idea is that instead of point sets (e.g. manifolds) one

Noncommutative geometry based on commutator expansions

We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization.

Missing the point in noncommutative geometry

It is shown that arbitrarily small regions are not definable in the formal sense, and how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry is investigated.

Noncommutative Geometry Year 2000

Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The discovery of quantum mechanics in the form of the noncommuting coordinates on the phase space of atomic

A Short survey of noncommutative geometry

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the

Short Steps in Noncommutative Geometry

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by

Spectral Geometry

  • B. Iochum
  • Mathematics
    Lectures on the Geometry of Manifolds
  • 2020
The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum

Superconformal nets and noncommutative geometry

This paper provides a further step in our program of studying superconformal nets over S^1 from the point of view of noncommutative geometry. For any such net A and any family Delta of localized

Projective Group Algebras

In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the M



Gravity coupled with matter and the foundation of non-commutative geometry

We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds. Its unitary representations correspond

Quantum Groups

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions

Twisted SU (2) group. An example of a non-commutative differential calculus

Pour un nombre ν de l'intervalle [−1, 1], on introduit et on etudie une C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν

Extensions of C*-algebras and K-homology

Free probability theory, Amer

  • Math. Soc
  • 1996

Homology of matrix algebras over rings and the Hochschild cohomology, Uspekhi Mat

  • Nauk
  • 1983

Noncommutative differential geometry

  • Inst. Hautes Études Sci. Publ. Math
  • 1986