@article {2007,
title = {Dirac operators on all Podles quantum spheres},
journal = {J. Noncomm. Geom. 1 (2007) 213-239},
number = {arXiv.org;math/0606480v2},
year = {2007},
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.},
doi = {10.4171/JNCG/5},
url = {http://hdl.handle.net/1963/2177},
author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi and Elmar Wagner}
}
@article {2005,
title = {The Dirac operator on SU_q(2)},
journal = {Commun. Math. Phys. 259 (2005) 729-759},
number = {arXiv:math/0411609;},
year = {2005},
note = {v2: minor changes},
publisher = {Springer},
abstract = {We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the
spectrum of the operator D is the same as that of the usual Dirac operator on
the 3-dimensional round sphere. The presence of an equivariant real structure J
demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.},
doi = {10.1007/s00220-005-1383-9},
url = {http://hdl.handle.net/1963/4425},
author = {Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Walter van Suijlekom and Joseph C. Varilly}
}