Dirac operators on all Podles quantum spheres
Abstract
We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of Uq(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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