K-theory, Cyclic Cohomology and Pairings for Quantum Heisenberg Manifolds

TL;DR

This paper computes K-theory and cyclic cohomology pairings for Quantum Heisenberg Manifolds, providing explicit bases and linking K-theory with cyclic homology, advancing understanding of their algebraic structure.

Contribution

It explicitly calculates pairings between K-theory and cyclic cohomology for QHM, and determines their periodic cyclic (co)homology with explicit bases, extending prior results.

Findings

Explicit bases for periodic cyclic cohomology of QHM.

Computed pairings between K-theory and cyclic cohomology.

Determined periodic cyclic homology and cohomology of QHM.

Abstract

The C*-algebras called Quantum Heisenberg Manifolds (QHM) were introduced by Rieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. 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.