Francesco D'Andrea, Ludwik Dabrowski, Giovanni Landi, Elmar Wagner
Dirac Operators on all Podles Quantum Spheres
The paper is published: J. Noncomm. Geom. 1 (2007) 213-239

MSC:

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

Abstract: We construct spectral triples on all Podle\'s quantum spheres ${S}^2_{qt}$.
These noncommutative geometries are equivariant for a left action of $\su$ and are regular,
even and of metric dimension~$2$. They are all isospectral to the undeformed round geometry of the sphere $S^2$.
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