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Quantum poincaré group for isotropic quantum space-time

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Possibilities of isotropic deformation of space-time are studied. The result is the two-parameter deformation. A differential calculus on the quantum space-time is constructed and the quantum differential geometry is formulated. A group of rigid motion of quantum space-time is investigated. This group is an example of a quantized braided group.

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  1. [1]

    Rembieliński J.: Quantum braided Poincaré group. Preprint KFT UL 7/93, Lódź Univ., 1993.

  2. [2]

    Manin Yu. I.: Quantum Groups and Non-Commutative Geometry. Centre de Recherches Mathématiques, Montreal, 1988.

  3. [3]

    Lukierski J., Nowicki A., Ruegg H., and Tolstoy V. N.: Phys. Lett. B264 (1991) 331.

  4. [4]

    Lukierski J., Nowicki A., and Ruegg H.: Phys. Lett. B293 (1992) 344.

  5. [5]

    Zakrzewski S.: J. Phys. A27 (1994) 2075.

  6. [6]

    Wess J. and Zumino B.: Nuclear Phys. (Proc. Suppl.) B18 (1990) 302.

  7. [7]

    Brzeziński T., Dąbrowski H., and Rembieliński J.: J. Math, Phys.33 (1992) 19.

  8. [8]

    Majid S.: J. Math. Phys.32 (1991) 3246.

  9. [9]

    Majid S.: J. Math. Phys.34 (1993) 2045.

  10. [10]

    Majid S.: Math. Proc. Cambr. Phil. Soc.113 (1993) 45.

  11. [11]

    Hlavatý L.: J. Math. Phys.35 (1994) 2560.

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This work is supported under the KBN grant No. 2P3.02.21706 p. 01.

I am grateful for an encouragement and many interesting discussions to J. Rembieliński. I would also like to thank J. Lukierski and P. Maślanka for the discussion during the 3rd Colloquium on Quantum Groups in Prague.

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Smoliński, K.A. Quantum poincaré group for isotropic quantum space-time. Czech J Phys 44, 1101–1107 (1994). https://doi.org/10.1007/BF01690462

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  • Differential Geometry
  • Braided Group
  • Rigid Motion
  • Differential Calculus
  • Isotropic Quantum