Dirac Operators on Quantum Flag Manifolds

Details Dirac Operators on Quantum Flag Manifolds Dirac Operators on Quantum Flag Manifolds

2003-05-05

arxiv.org/abs/math/0305071v3

Mathematics

Quantum Algebra

10 pages

Scientific paper

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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