On the absence of continuous symmetries for noncommutative 3-spheres

Fedele Lizzi, Allen Stern, Patrizia Vitale
2005 Journal of Mathematical Physics  
A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whether or not this property can be extended to the noncommutative three-spheres of Connes and
more » ... s and Dubois-Violette. Upon restricting to quantum groups which are continuous deformations of Spin(4) and SO(4) with standard co-actions, our results suggest that this is not the case.
doi:10.1063/1.2070087 fatcat:zpuuftd65vd7fohepdpszssk3u