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Tensor representation of the quantum groupSL q (2,C) and quantum Minkowski space

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Zeitschrift für Physik C Particles and Fields

Abstract

We investigate the structure of the tensor product representation of the quantum groupSL q (2,C) by using the 2-dimensional quantum plane as a building block. Two types of 4-dimensional spaces are constructed applying the methods used in twistor theory. We show that the 4-dimensional real representation ofSL q (2,C) generates a consistent non-commutative algebra, and thus it provides a quantum deformation of Minkowski space. The transformation of this 4-dimensional space gives the quantum Lorentz groupSO q(3, 1).

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Author notes

  1. S. Watamura

    Present address: Department of Physics, College of General Education, Tohoku University, Kawauchi, 980, Sendai, Japan

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe, Federal Republic of Germany

    U. Carow-Watamura, M. Schlieker, M. Scholl & S. Watamura

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  1. U. Carow-Watamura
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  2. M. Schlieker
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  3. M. Scholl
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  4. S. Watamura
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Carow-Watamura, U., Schlieker, M., Scholl, M. et al. Tensor representation of the quantum groupSL q (2,C) and quantum Minkowski space. Z. Phys. C - Particles and Fields 48, 159–165 (1990). https://doi.org/10.1007/BF01565619

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  • DOI: https://doi.org/10.1007/BF01565619

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