Quantum automorphism groups and SO(3)-deformations

Abstract

We show that any compact quantum group having the same fusion rules as the ones of $SO(3)$ is the quantum automorphism group of a pair $(A,\phi )$, where $A$ is a finite dimensional $C^{\ast }$-algebra endowed with a homogeneous faithful state. We also study the representation category of the quantum automorphism group of $(A,\phi )$ when $\phi$ is not necessarily positive, generalizing some known results, and we discuss the possibility of classifying the cosemisimple (not necessarily compact) Hopf algebras whose corepresentation semi-ring is isomorphic to that of $SO(3)$.

Comments are welcome

References in corpus (1)

• Introduction to quantum groups