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The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra

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Zeitschrift für Physik C Particles and Fields

Abstract

The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation ofGL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant and inverse are constructed. A right-invariant differential calculus is presented and the role of the different deformation parameters investigated. While the corresponding Lie algebra relations are simply deformed, the comultiplication exhibits both quantization parameters.

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Author notes

  1. A. Schirrmacher

    Present address: II. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Karlsruhe, W-7500, Karlsruhe, Federal Republic of Germany

    A. Schirrmacher & J. Wess

  2. Department of Physics, University of California, Berkeley, CA, USA

    B. Zumino

  3. CERN, CH-1211, Genéva 23, Switzerland

    B. Zumino

Authors
  1. A. Schirrmacher
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  2. J. Wess
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  3. B. Zumino
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Schirrmacher, A., Wess, J. & Zumino, B. The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra. Z. Phys. C - Particles and Fields 49, 317–324 (1991). https://doi.org/10.1007/BF01555507

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  • DOI: https://doi.org/10.1007/BF01555507

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