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Dirac Operators on Quantum Flag Manifolds

Ulrich Kraehmer
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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 Podles' quantum sphere one obtains the spectral triple found by L. Dabrowski and A. Sitarz.

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Ulrich Kraehmer. 2003-06-18. Dirac Operators on Quantum Flag Manifolds. https://arxiv.org/abs/math/0305071

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