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Finite Noncommutative Spaces

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Noncommutative Geometry and Particle Physics

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Abstract

In this chapter (and the next) we consider only finite discrete topological spaces. However, we will stretch their usual definition, which is perhaps geometrically not so interesting

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References

  1. Kasparov, G.G.: The operator \(K\)-functor and extensions of \(C^{\ast } \)-algebras. Izv. Akad. Nauk SSSR Ser. Mat. 44, 571–636, 719 (1980)

    Google Scholar 

  2. Blackadar, B.: K-Theory for Operator Algebras. Mathematical Sciences Research Institute Publications, Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  3. Landsman, N.P.: Mathematical Topics between Classical and Quantum Mechanics. Springer, New York (1998)

    Book  Google Scholar 

  4. Morita, K.: Duality for modules and its applications to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6, 83–142 (1958)

    Google Scholar 

  5. Rieffel, M.A.: Morita equivalence for \(C^{\ast } \)-algebras and \(W^{\ast } \)-algebras. J. Pure Appl. Algebra 5, 51–96 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Raeburn, I., Williams, D.P.: Morita Equivalence and Continuous-trace \(C^*\)-algebras, Volume 60 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (1998)

    Google Scholar 

  7. Iochum, B., Krajewski, T., Martinetti, P.: Distances in finite spaces from noncommutative geometry. J. Geom. Phys. 37, 100–125 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Connes, A.: On the spectral characterization of manifolds. J. Noncommut. Geom. 7, 1–82 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Etingof, P., Golberg, O., Hensel, S., Liu, T., Schwendner, A., Vaintrob, D., Yudovina, E.: Introduction to Representation Theory, Volume 59 of Student Mathematical Library. American Mathematical Society, Providence, RI (2011) (With historical interludes by Slava Gerovitch)

    Google Scholar 

  10. Landi, G.: An Introduction to Noncommutative Spaces and their Geometry. Springer, Berlin (1997)

    Google Scholar 

  11. André, Y.: Différentielles non commutatives et théorie de Galois différentielle ou aux différences. Ann. Sci. École Norm. Sup. 34(4), 685–739 (2001)

    Google Scholar 

  12. Connes, A., Marcolli, M.: Noncommutative Geometry. Quantum Fields and Motives. AMS, Providence (2008)

    Google Scholar 

  13. Venselaar, J.J.: Classification and equivalences of noncommutative tori and quantum lens spaces. PhD thesis, Utrecht University (2012)

    Google Scholar 

  14. Connes, A., Skandalis, G.: The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20, 1139–1183 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  15. Landsman, N.P.: Quantized Reduction as a Tensor Product. In: Quantization of Singular Symplectic Quotients, Volume 198 of Program Mathematics, pp. 137–180, Birkhäuser, Basel (2001)

    Google Scholar 

  16. Mesland, B.: Bivariant \(K\)-theory of groupoids and the noncommutative geometry of limit sets. PhD thesis, Universität Bonn (2009)

    Google Scholar 

  17. Mesland, B.: Unbounded bivariant K-theory and correspondences in noncommutative geometry. J. Reine Angew. Math. 691, 101–172 (2014)

    Google Scholar 

  18. Marcolli, M., van Suijlekom, W.D.: Gauge networks in noncommutative geometry. J. Geom. Phys. 75, 71–91 (2014)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Correspondence to Walter D. van Suijlekom .

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van Suijlekom, W.D. (2015). Finite Noncommutative Spaces. In: Noncommutative Geometry and Particle Physics. Mathematical Physics Studies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9162-5_2

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