Geometrical Structures on Noncommutative Spaces

  • Olivier Grandjean
Part of the Mathematical Physics Studies book series (MPST, volume 23)


We review the connection between supersymmetric quantum mechanics and differential geometry. This gives a formulation of differential geometry that is well suited for generalization to the noncommutative setting. Two examples are presented. First, we show how the quantum target of the Wess-Zumino-Witten model on SU(2) can be encoded into ’N = 1 spectral data’. Then, we explain how the Kähler structure on the noncommutative two-torus can be constructed starting with N = 1 spectral data.

Mathematics Subject Classification (2000)

81T40 81T70 81T75 

Key words

noncommutative geometry differential geometry Wess-Zumino-Witten model 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Olivier Grandjean
    • 1
  1. 1.Harvard UniversityCambridgeUSA

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