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Spectral Triples and Associated Connes-de Rham Complex for the Quantum SU(2) and the Quantum Sphere

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Abstract

In this article, we construct spectral triples for the C *-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There have been various approaches towards building a calculus on quantum spaces, but there seem to be very few instances of computations outlined in Chapter 6, [5]. We give detailed computations of the associated Connes-de Rham complex and the space of L 2 -forms.

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Authors and Affiliations

  1. Indian Statistical Institute, 203, B. T. Road, Calcutta, 700 108, India

    Partha Sarathi Chakraborty

  2. Indian Statistical Institute, 7, SJSS Marg, New Delhi, 110 016, India

    Arupkumar Pal

Authors
  1. Partha Sarathi Chakraborty
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  2. Arupkumar Pal
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Correspondence to Arupkumar Pal.

Additional information

Communicated by A. Connes

The first author would like to acknowledge support from the National Board for Higher Mathematics, India.

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Chakraborty, P., Pal, A. Spectral Triples and Associated Connes-de Rham Complex for the Quantum SU(2) and the Quantum Sphere. Commun. Math. Phys. 240, 447–456 (2003). https://doi.org/10.1007/s00220-003-0921-6

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  • DOI: https://doi.org/10.1007/s00220-003-0921-6

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