On the structure of quantum automorphism groups.(English)Zbl 1376.81041
Summary: We compute the \(K\)-theory of quantum automorphism groups of finite-dimensional \(C^{*}\)-algebras in the sense of Wang. The results show in particular that the reduced \(C^{*}\)-algebras of functions on the quantum permutation groups \(S_{n}^{+}\) are pairwise non-isomorphic for different values of \(n\). Along the way we discuss some general facts regarding torsion in discrete quantum groups. In fact, the duals of quantum automorphism groups are the most basic examples of discrete quantum groups exhibiting genuine quantum torsion phenomena.
MSC:
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 19K14 | \(K_0\) as an ordered group, traces |
| 58B32 | Geometry of quantum groups |
Cite
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