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Principal Fibrations from Noncommutative Spheres

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We construct noncommutative principal fibrations S θ 7→S θ 4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. “The algebra inclusion is an example of a not-trivial quantum principal bundle.”

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/b, 34127, Trieste, Italy

    Giovanni Landi

  2. INFN, Sezione di Napoli, Napoli, Italy

    Giovanni Landi

  3. Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014, Trieste, Italy

    Walter van Suijlekom

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  1. Giovanni Landi
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  2. Walter van Suijlekom
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Correspondence to Giovanni Landi.

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Communicated by A. Connes

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Landi, G., Suijlekom, W. Principal Fibrations from Noncommutative Spheres. Commun. Math. Phys. 260, 203–225 (2005). https://doi.org/10.1007/s00220-005-1377-7

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  • DOI: https://doi.org/10.1007/s00220-005-1377-7

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