Dirac operators on all Podles quantum spheres

Details Dirac operators on all Podles quantum spheres Dirac operators on all Podles quantum spheres

2006-06-20

arxiv.org/abs/math/0606480v2

J. Noncomm. Geom. 1 (2007) 213-239

Mathematics

Quantum Algebra

24 pages, no figures; v2: minor corrections

Scientific paper

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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