Spectral triples and associated Connes-de Rham complex for the quantum SU(2) and the quantum sphere

Abstract

In this article, we construct spectral triples for the C^∗-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There have been various approaches towards building a calculus on quantum spaces, but there seem to be very few instances of computations outlined in Chapter 6, [5]. We give detailed computations of the associated Connes-de Rham complex and the space of L₂-forms.