The Fundamental Group of a Noncommutative Space

  title={The Fundamental Group of a Noncommutative Space},
  author={Walter D. van Suijlekom and Jeroen Winkel},
  journal={Algebras and Representation Theory},
We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded algebras and show that the category of flat connections on such modules forms a Tannakian category. As such this category can be realised as the category of representations of an affine group scheme G , which in the classical case is (the pro-algebraic completion… 



Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations

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

Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples

Abstract: We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete

Universal covering space of the noncommutative torus

Gelfand - Na\u{i}mark theorem supplies contravariant functor from a category of commutative $C^*-$ algebras to a category of locally compact Hausdorff spaces. Therefore any commutative $C^*-$ algebra

Projective Modules over Higher-Dimensional Non-Commutative Tori

  • M. Rieffel
  • Mathematics
    Canadian Journal of Mathematics
  • 1988
The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus Tn with its algebra, C(Tn), of


We study canonical operation of the Lie algebra Der(#7B-A) of derivations of an algebra #7B-A with a unit in the graded differential algebra Ω(#7B-A). We introduce different graded differential

Spectral sequences for Hochschild cohomology and graded centers of derived categories

The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We

Holomorphic Structures on the Quantum Projective Line

We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere—which, with additional structures, we identify