@article {2008,
title = {Noncommutative families of instantons},
journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038},
number = {arXiv.org;0710.0721v2},
year = {2008},
publisher = {Oxford University Press},
abstract = {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 $Sp_\\\\theta(2)$.},
doi = {10.1093/imrn/rnn038},
url = {http://hdl.handle.net/1963/3417},
author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom}
}
@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}
}
@article {2005,
title = {The local index formula for SUq(2)},
journal = {K-Theory 35 (2005) 375-394},
number = {SISSA;01/2005/FM},
year = {2005},
abstract = {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.},
doi = {10.1007/s10977-005-3116-4},
url = {http://hdl.handle.net/1963/1713},
author = {Walter van Suijlekom and Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Joseph C. Varilly}
}
@article {2005,
title = {Principal fibrations from noncommutative spheres},
journal = {Comm. Math. Phys. 260 (2005) 203-225},
number = {SISSA;68/2004/FM},
year = {2005},
abstract = {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.},
doi = {10.1007/s00220-005-1377-7},
url = {http://hdl.handle.net/1963/2284},
author = {Giovanni Landi and Walter van Suijlekom}
}