TY - JOUR
T1 - Dirac operators on all Podles quantum spheres
JF - J. Noncomm. Geom. 1 (2007) 213-239
Y1 - 2007
A1 - Francesco D'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Elmar Wagner
AB - 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.
UR - http://hdl.handle.net/1963/2177
U1 - 2067
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The Dirac operator on SU_q(2)
JF - Commun. Math. Phys. 259 (2005) 729-759
Y1 - 2005
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Andrzej Sitarz
A1 - Walter van Suijlekom
A1 - Joseph C. Varilly
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/4425
N1 - v2: minor changes
U1 - 4175
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -