%0 Journal Article
%J Reviews in Mathematical Physics
%D 2018
%T Principal fibrations over noncommutative spheres
%A Michel Dubois-Violette
%A Xiao Han
%A Giovanni Landi
%X 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 Connesâ€“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.
%B Reviews in Mathematical Physics
%V 30
%P 1850020
%G eng
%U https://arxiv.org/abs/1804.07032
%R 10.1142/S0129055X18500204