Dirac Operators on Quantum Flag Manifolds
Ulrich Kraehmer
TL;DR
This paper constructs a Dirac operator on quantum flag manifolds, providing a spectral triple framework that generalizes previous results and connects to differential calculi in noncommutative geometry.
Contribution
It introduces a Dirac operator on quantized flag manifolds, linking it to covariant differential calculi and spectral triples, extending prior work in noncommutative geometry.
Findings
Dirac operator defined on quantum flag manifolds
Boundedness of differentials df=i[D,f] established
Spectral triple recovered for quantum sphere case
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons