The noncommutative Chern-Connes character of the locally compact quantum normalizer of SU(1, 1) in SL(2,C)

A locally compact quantum group analogue of the normalizer of SU(1,1) in SL(2,C)

S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky in 1994 and more recently by Woronowicz gave strong indications that the normalizer S̃U(1, 1) of SU(1, 1) in SL(2,C) is a much better quantization candidate than SU(1, 1) itself. In this paper we show that this is indeed the case by constructing S̃Uq(1, 1), a new examp...

Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations

We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of R. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features. The new examples include the instanton algebra and the NC-4-spheres S4 θ . We construct the noncommutative algebras A = C∞(S4 θ ) of functions on NCsphere...

ar X iv : h ep - t h / 01 01 09 3 v 1 1 5 Ja n 20 01 C ∗ algebras and Differential Geometry ∗

This is the translation to appear in the ”SUPERSYMMETRY 2000 Encyclopaedic Dictionary” of the original Comptes Rendus Note, published in March 1980, in which basic notions of noncommutative geometry were introduced and applied to noncommutative tori. These include connections on finite projective modules, their curvature, and the Chern character. Finite projective modules on the noncommutative ...

Connes-Chern character in relative K-homology

Lecture 1 (Pflaum): Title: Relative cohomology and its pairings Relative cyclic cohomology theory and its pairings turned out to be a powerful tool to explain crucial properties of certain invariants in global analysis such as for example the divisor flow. In this talk, the homological foundations for pairings in relative cyclic cohomology will be explained. Moreover, the relative Chern-charact...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras