Dirac Operators on Quantum Flag Manifolds
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- May 2003
- DOI:
- arXiv:
- arXiv:math/0305071
- Bibcode:
- 2003math......5071K
- Keywords:
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- Quantum Algebra
- E-Print:
- 10 pages