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 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.
VL - 30
UR - https://arxiv.org/abs/1804.07032
ER -