Quantum automorphism groups and SO(3)-deformations

Colin Mrozinski (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 $(A, \varphi)$, where $A$ is a finite dimensional $C^*$-algebra endowed with a homogeneous faithful state. We also study the representation category of the quantum automorphism group of $(A, \varphi)$ when $\varphi$ 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 $SO(3)$.

Mots clés: Quantum groups; monoidal categories; Hopf Algebras

Domaines: Algèbres quantiques [math.QA]

Colin Mrozinski. Quantum automorphism groups and SO(3)-deformations. 2013. ⟨hal-00805534v1⟩