Abstract
A Dirac operator D on quantized irreducible generalized flag manifolds is defined. This yields a Hilbert space realization of the covariant first-order differential calculi constructed by I. Heckenberger and S. Kolb. All differentials df=i[D,f] are bounded operators. In the simplest case of Podleś' quantum sphere one obtains the spectral triple found by L. Dabrowski and A. Sitarz.
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Krähmer>, U. Dirac Operators on Quantum Flag Manifolds. Letters in Mathematical Physics 67, 49–59 (2004). https://doi.org/10.1023/B:MATH.0000027748.64886.23
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DOI: https://doi.org/10.1023/B:MATH.0000027748.64886.23