TY - JOUR
T1 - Dirac operators on noncommutative principal circle bundles
Y1 - 2014
A1 - Andrzej Sitarz
A1 - Alessandro Zucca
A1 - Ludwik Dabrowski
AB - We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2.
PB - World Scientific Publishing
UR - http://urania.sissa.it/xmlui/handle/1963/35125
U1 - 35363
U2 - Mathematics
U4 - 1
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 -
TY - JOUR
T1 - Dirac operator on the standard Podles quantum sphere
JF - Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003
Y1 - 2001
A1 - Ludwik Dabrowski
A1 - Andrzej Sitarz
PB - SISSA Library
UR - http://hdl.handle.net/1963/1668
U1 - 2450
U2 - Mathematics
U3 - Mathematical Physics
ER -