Non existence of group structure on some quantum spaces

Abstract

We prove that some well known compact quantum spaces like quantum tori and some quantum two-spheres do not admit a compact quantum group structure. This is achieved by considering existence of traces, characters and nuclearity of the corresponding ${\mathrm{C}}^{\ast }$-algebras.

Short and simple

References in corpus (2)

• Quantum families of maps and quantum semigroups on finite quantum spaces
• Quantum $\mathrm{SO}(3)$ groups and quantum group actions on $M_2$