# K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds

### Olivier Gabriel

Université Denis Diderot Paris 7, France

## Abstract

The C*-algebras called quantum Heisenberg manifolds (QHMs) were introduced by Rieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. It was later shown that they are also examples of generalized crossed products. In this article, we compute the pairings of K-theory and cyclic cohomology on the QHM. Combining these calculations with other results proved elsewhere, we also determine the periodic cyclic homology and cohomology of these algebras, and obtain explicit bases of the periodic cyclic cohomology of the QHM. We further isolate bases of periodic cyclic homology, expressed as Chern characters of the K-theory.

## Cite this article

Olivier Gabriel, K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds. J. Noncommut. Geom. 7 (2013), no. 2, pp. 301–333

DOI 10.4171/JNCG/118