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Quantum group gauge theory on quantum spaces

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Abstract

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including aq-deformed Dirac monopole on the quantum sphere of Podles with quantum differential structure coming from the 3D calculus of Woronowicz onSU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fibre, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces).

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Author notes

  1. Shahn Majid (SERC Fellow and Drapers Fellow)

    Present address: Pembroke College, Cambridge

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW, U.K.

    Thomasz Brzeziński & Shahn Majid (SERC Fellow and Drapers Fellow)

Authors
  1. Thomasz Brzeziński
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  2. Shahn Majid
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Additional information

Communicated by A. Connes

Supported by St. John's College, Cambridge and KBN grant 202189101

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Brzeziński, T., Majid, S. Quantum group gauge theory on quantum spaces. Commun.Math. Phys. 157, 591–638 (1993). https://doi.org/10.1007/BF02096884

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  • DOI: https://doi.org/10.1007/BF02096884

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