"Vector bundles" over quantum Heisenberg manifolds

TL;DR

This paper uses Morita equivalence techniques to construct finitely generated projective modules over quantum Heisenberg manifolds, providing insights into their K-theoretic trace range related to the deformation Poisson bracket.

Contribution

It introduces a method to analyze projective modules over quantum Heisenberg manifolds using Morita equivalence, linking K-theory to deformation parameters.

Findings

Identification of finitely generated projective modules

Determination of trace range in K_{0}-group

Connection to Poisson bracket deformation

Abstract

By means of techniques from the Morita equivalence theory, we get finitely generated and projective modules over the quantum Heisenberg manifolds. This enables us to get some information about the range of the trace of these algebras, at the level of the K_{0}-group, in terms of the Poisson bracket in whose direction the manifolds are deformed.