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Dirac operators on all Podles quantum spheres

TitleDirac operators on all Podles quantum spheres
Publication TypeJournal Article
Year of Publication2007
AuthorsD'Andrea, F, Dabrowski, L, Landi, G, Wagner, E
JournalJ. Noncomm. Geom. 1 (2007) 213-239

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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