TY - JOUR T1 - Principal fibrations over noncommutative spheres JF - Reviews in Mathematical Physics Y1 - 2018 A1 - Michel Dubois-Violette A1 - Xiao Han A1 - Giovanni Landi AB - We present examples of noncommutative four-spheres that are base spaces of $SU(2)$-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of $SU(2)$. We give conditions for the components of the Connes–Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres. VL - 30 UR - https://arxiv.org/abs/1804.07032 ER - TY - CHAP T1 - Pimsner Algebras and Circle Bundles T2 - Noncommutative Analysis, Operator Theory and Applications Y1 - 2016 A1 - Francesca Arici A1 - Francesco D'Andrea A1 - Giovanni Landi ED - Alpay, Daniel ED - Cipriani, Fabio ED - Colombo, Fabrizio ED - Guido, Daniele ED - Sabadini, Irene ED - Sauvageot, Jean-Luc AB -

We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

JF - Noncommutative Analysis, Operator Theory and Applications PB - Springer International Publishing CY - Cham SN - 978-3-319-29116-1 UR - https://doi.org/10.1007/978-3-319-29116-1_1 ER - TY - JOUR T1 - Pimsner algebras and Gysin sequences from principal circle actions JF - Journal of Noncommutative Geometry Y1 - 2016 A1 - Francesca Arici A1 - Jens Kaad A1 - Giovanni Landi VL - 10 UR - http://hdl.handle.net/2066/162951 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 -