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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2015

Quantum automorphism groups and SO(3)-deformations

Colin Mrozinski
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Résumé

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 $SO(3)$.
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Dates et versions

hal-00805534 , version 1 (28-03-2013)
hal-00805534 , version 2 (06-01-2014)

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Colin Mrozinski. Quantum automorphism groups and SO(3)-deformations. Journal of Pure and Applied Algebra, 2015, 219 (1), ⟨10.1016/j.jpaa.2014.04.006⟩. ⟨hal-00805534v2⟩
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