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Fixed Point Algebras for Easy Quantum Groups
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their $K$-groups. Building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the $K$-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group $S_n^+$, the free orthogonal quantum group $O_n^+$ and the quantum reflection groups $H_n^{s+}$. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups, which are related to Hopf–Galois extensions.
Keywords: $K$-theory; Kirchberg algebras; easy quantum groups; noncrossing partitions; fusion rules; free actions; free orthogonal quantum groups; quantum permutation groups; quantum reflection groups. 
@article{SIGMA_2016_12_a96,
     author = {Olivier Gabriel and Moritz Weber},
     title = {Fixed {Point} {Algebras} for {Easy} {Quantum} {Groups}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2016},
     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a96/}
}
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Olivier Gabriel; Moritz Weber. Fixed Point Algebras for Easy Quantum Groups. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a96/

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