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Communications in Mathematical Physics

, Volume 330, Issue 3, pp 1327–1337 | Cite as

Yang–Mills on Quantum Heisenberg Manifolds

  • Partha Sarathi ChakrabortyEmail author
  • Satyajit Guin
Article

Abstract

In the noncommutative geometry program of Connes, there are two variations of the concept of the Yang–Mills action functional. We show that for the quantum Heisenberg manifolds for generic parameter values they agree.

Keywords

Heisenberg Group Projective Module Noncommutative Geometry Triangular Matrice Hermitian Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Chakraborty P.S., Sinha K.B.: Geometry on the quantum Heisenberg manifold. J. Funct. Anal. 203(2), 425–452 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Connes A.: C*-algèbres et géométrie differentielle. C. R. Acad. Sci. Paris Ser. A-B 290(13), A599–A604 (1980)MathSciNetGoogle Scholar
  3. 3.
    Connes A., Rieffel M.A.: Yang–Mills for non-commutative two-tori. Contemp. Math. 62, 237–266 (1987)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Connes A.: Noncommutative Geometry. Academic Press, London (1994)zbMATHGoogle Scholar
  5. 5.
    Kang S.: The Yang–Mills functional and Laplace’s equation on quantum Heisenberg manifolds. J. Funct. Anal. 258(1), 307–327 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Lee H.H.: On the moduli space of a quantum Heisenberg manifold. J. Funct. Anal. 263(4), 941–959 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Rieffel M.A.: Deformation quantization of Heisenberg manifolds. Commun. Math. Phys. 122, 531–562 (1989)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.The Institute of Mathematical SciencesTaramani, ChennaiIndia

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