Moduli Space and Structure of Noncommutative 3-spheres

  title={Moduli Space and Structure of Noncommutative 3-spheres},
  author={Alain Connes and Michel DUBOIS-VIOLETTE},
We analyse the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and prove a general algebraic result which considerably refines the classical homomorphism from a quadratic algebra to a cross-product algebra associated to the characteristic variety and lands in a richer cross-product. It allows to control the C∗-norm on involutive quadratic algebras and to construct the differential calculus in the desired… CONTINUE READING
Highly Cited
This paper has 29 citations. REVIEW CITATIONS
23 Citations
13 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 13 references

Some algebraic structures connected with the Yang- Baxter equation

  • E. K. Sklyanin
  • Representation of quantum algebras. Func. Anal…
  • 1983
Highly Influential
8 Excerpts

Noncommutative differential geometry. Part I: The Chern character in K-homology; Part II: de Rham homology and noncommutative algebra

  • A. Connes
  • Preprints IHES M/82/53;
  • 1982
Highly Influential
7 Excerpts

Regularity of the four dimensional Sklyanin algebra

  • S. P. Smith, J. T. Stafford
  • Compos. Math.,
  • 1992
Highly Influential
5 Excerpts

Some algebras associated to automorphisms of elliptic curves

  • M. Artin, J. Tate, M. Van den Bergh
  • The Grothendieck Festschrift. vol. I. Prog. Math…
  • 1990
Highly Influential
4 Excerpts

Sklyanin elliptic algebras

  • A. V. Odesskii, B. L. Feigin
  • Func. Anal. Appl.,
  • 1989
Highly Influential
4 Excerpts

Homological properties of Sklyanin algebras

  • J. Tate, M. Van den Bergh
  • Invent. Math.,
  • 1996
1 Excerpt

Similar Papers

Loading similar papers…