Abstract
Following Woronowicz's proposal the bicovariant differential calculus on the quantum groupsSU q (N) andSO q (N) is constructed. A systematic construction of bicovariant bimodules by using the\(\hat R_q \) matrix is presented. The relation between the Hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules, and theq-deformed universal enveloping algebras is given. Imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined. As an application the Maurer-Cartan equations and theq-analogue of the structure constants are formulated.
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Communicated by A. Connes
Address after 1 Dec. 1990, Institute of Theoretical Physics, University of München.
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Carow-Watamura, U., Schlieker, M., Watamura, S. et al. Bicovariant differential calculus on quantum groupsSU q (N) andSO q (N) . Commun.Math. Phys. 142, 605–641 (1991). https://doi.org/10.1007/BF02099103
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DOI: https://doi.org/10.1007/BF02099103