Document Type
Journal Article
RIS ID
38962
Citation
Kang, Sooran, 2010, The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds, Journal of Functional Analysis, 258(1), 307-327.
http://ro.uow.edu.au/era/1276
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.