Bounded and unbounded Fredholm modules for quantum projective spaces

TL;DR

This paper constructs explicit K-theory and K-homology generators for quantum projective spaces and sketches a method to build Dirac-like operators and spectral triples of arbitrary positive dimension.

Contribution

It provides explicit generators for K-theory and K-homology of quantum projective spaces and introduces a construction approach for unbounded Fredholm modules of any positive real dimension.

Findings

Explicit generators for K-theory and K-homology of quantum projective spaces.

A method to construct Dirac-like operators and spectral triples of any positive real dimension.

Abstract

We construct explicit generators of the K-theory and K-homology of the coordinate algebra of `functions' on quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Dirac-like operators and spectral triples of any positive real dimension.