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Letters in Mathematical Physics

, Volume 67, Issue 1, pp 49–59 | Cite as

Dirac Operators on Quantum Flag Manifolds

  • Ulrich Krähmer>
Article

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.

noncommutative geometry quantum homogeneous spaces 
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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ulrich Krähmer>
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany

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