@article {doi:10.1142/S0129055X18500204,
title = {Principal fibrations over noncommutative spheres},
journal = {Reviews in Mathematical Physics},
volume = {30},
number = {10},
year = {2018},
pages = {1850020},
abstract = {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{\textendash}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.},
doi = {10.1142/S0129055X18500204},
url = {https://arxiv.org/abs/1804.07032},
author = {Michel Dubois-Violette and Xiao Han and Giovanni Landi}
}