On the moduli space of a quantum Heisenberg manifold

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