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Article
The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds
Journal of Functional Analysis
  • Sooran Kang, University of Wollongong
Document Type
Journal Article
Publication Date
1-1-2010
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.

RIS ID
38962
Citation Information
Sooran Kang. "The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds" Journal of Functional Analysis Vol. 258 Iss. 1 (2010) p. 307 - 327
Available at: http://works.bepress.com/skang/1/