Abstract
In this paper, we discuss the Yang–Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that gives rise to critical points of the Yang–Mills functional. Moreover, we show that there is a relationship between this particular family of critical points of the Yang–Mills functional and Laplace's equation on multiplication-type, skew-symmetric elements of quantum Heisenberg manifolds; recall that Laplacian is the leading term for the coupled set of equations making up the Yang–Mills equation.
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