TY - JOUR
T1 - Noncommutative families of instantons
JF - Int. Math. Res. Not. vol. 2008, Article ID rnn038
Y1 - 2008
A1 - Giovanni Landi
A1 - Chiara Pagani
A1 - Cesare Reina
A1 - Walter van Suijlekom
AB - We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/3417
U1 - 918
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 -
TY - JOUR
T1 - The local index formula for SUq(2)
JF - K-Theory 35 (2005) 375-394
Y1 - 2005
A1 - Walter van Suijlekom
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Andrzej Sitarz
A1 - Joseph C. Varilly
AB - We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.
UR - http://hdl.handle.net/1963/1713
U1 - 2438
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Principal fibrations from noncommutative spheres
JF - Comm. Math. Phys. 260 (2005) 203-225
Y1 - 2005
A1 - Giovanni Landi
A1 - Walter van Suijlekom
AB - We construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.
UR - http://hdl.handle.net/1963/2284
U1 - 1732
U2 - Mathematics
U3 - Mathematical Physics
ER -