On the moduli space of a quantum Heisenberg manifold ✩

We investigate the Yang–Mills problem on a quantum Heisenberg manifold Dc μν in the setting of the noncommutative differential geometry. This problem was already studied by Kang (2010) in [6] for a specific module Ξ over Dc μν, and Kang obtained a family of connections which are critical points of the Yang–Mills functional on Ξ. But it turned out that they are neither minima nor maxima. In this article we construct a connection ∇0 on Ξ, and show that it is a minimum of the Yang–Mills functional on the module. Moreover we give a certain family of minima including ∇0, and show that the moduli space for Ξ is non-trivial. © 2012 Elsevier Inc. All rights reserved.