Quantum Group of Isometries in Classical and Noncommutative Geometry

  title={Quantum Group of Isometries in Classical and Noncommutative Geometry},
  author={Debashish Goswami},
  journal={Communications in Mathematical Physics},
  • Debashish Goswami
  • Published 2008
  • Mathematics, Physics
  • Communications in Mathematical Physics
  • We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold… CONTINUE READING
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