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Dirac operators on all Podles quantum spheres

Ludwik Dabrowski·Francesco D'Andrea·Giovanni Landi·Elmar Wagner
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Abstract

We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. 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.

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Ludwik Dabrowski, Francesco D'Andrea, Giovanni Landi, Elmar Wagner. 2007-01-22. Dirac operators on all Podles quantum spheres. https://arxiv.org/abs/math/0606480

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