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Complex quantum group, dual algebra and bicovariant differential calculus

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Abstract

The method used to construct the bicovariant bimodule in ref. [CSWW] is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group. The complex quantum group Fun q (SL(N, C)) is defined by requiring that it contains Fun q (SU(N)) as a subalgebra analogously to the quantum Lorentz group. Analyzing the properties of the fundamental bimodule, we show that the dual algebra has the structure of the twisted product Fun q (SU(N))⊗Fun q (SU(N)) *reg . Then the bicovariant differential calculi on the complex quantum group are constructed.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, Tohoku University, 980, Sendai, Japan

    Ursula Carow-Watamura

  2. Department of Physics, College of General Education, Tohoku University, 980, Sendai, Japan

    Satoshi Watamura

Authors
  1. Ursula Carow-Watamura
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  2. Satoshi Watamura
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Communicated by H. Araki

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Carow-Watamura, U., Watamura, S. Complex quantum group, dual algebra and bicovariant differential calculus. Commun.Math. Phys. 151, 487–514 (1993). https://doi.org/10.1007/BF02097024

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  • DOI: https://doi.org/10.1007/BF02097024

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