Journal of Noncommutative Geometry

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Volume 1, Issue 2, 2007, pp. 213–239
DOI: 10.4171/JNCG/5

Dirac operators on all Podleś quantum spheres

Francesco D'Andrea[1], Ludwik Dąbrowski[2], Giovanni Landi[3] and Elmar Wagner[4]

(1) SISSA, Trieste
(2) SISSA, Trieste
(3) University of Trieste
(4) University of Trieste

We construct spectral triples on all Podleś quantum spheres S2qt. These noncommutative geometries are equivariant for a left action of $\mathcal{U}$q(su(2)) and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the sphere S2. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.

Keywords: Noncommutative geometry, spectral triples, quantum groups, quantum spheres

D'Andrea Francesco, Dąbrowski Ludwik, Landi Giovanni, Wagner Elmar: Dirac operators on all Podleś quantum spheres. J. Noncommut. Geom. 1 (2007), 213-239. doi: 10.4171/JNCG/5