@article {2008,
title = {The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere},
journal = {Comm. Math. Phys. 279 (2008) 77-116},
number = {SISSA;95/2007/MP},
year = {2008},
abstract = {Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an {\textquoteleft}instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of {\textquoteleft}infinitesimals\\\' is also introduced.},
doi = {10.1007/s00220-008-0420-x},
url = {http://hdl.handle.net/1963/2567},
author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi}
}
@article {2002,
title = {Instanton algebras and quantum 4-spheres},
journal = {Differential Geom. Appl. 16 (2002) 277-284},
number = {arXiv.org;math/0101177v2},
year = {2002},
publisher = {Elsevier},
abstract = {We study some generalized instanton algebras which are required to describe {\textquoteleft}instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form.},
doi = {10.1016/S0926-2245(02)00066-9},
url = {http://hdl.handle.net/1963/3134},
author = {Ludwik Dabrowski and Giovanni Landi}
}
@article {2001,
title = {Instantons on the Quantum 4-Spheres S^4_q},
journal = {Comm. Math. Phys. 221 (2001) 161-168},
number = {arXiv.org;math/0012103v2},
year = {2001},
publisher = {Springer},
abstract = {We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.},
doi = {10.1007/PL00005572},
url = {http://hdl.handle.net/1963/3135},
author = {Ludwik Dabrowski and Giovanni Landi and Tetsuya Masuda}
}