Fixed point algebras for easy quantum groups
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Fixed point algebras for easy quantum groups. / Gabriel, Olivier; Weber, Moritz.
I: Symmetry, Integrability and Geometry: Methods and Applications, Bind 12, 097, 2016.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Fixed point algebras for easy quantum groups
AU - Gabriel, Olivier
AU - Weber, Moritz
PY - 2016
Y1 - 2016
N2 - 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 Hs+ n. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions.
AB - 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 Hs+ n. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions.
KW - Easy quantum groups
KW - Free actions
KW - Free orthogonal quantum groups
KW - Fusion rules
KW - K-theory
KW - Kirchberg algebras
KW - Noncrossing partitions
KW - Quantum permutation groups
KW - Quantum reflection groups
UR - http://www.scopus.com/inward/record.url?scp=84996555070&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2016.097
DO - 10.3842/SIGMA.2016.097
M3 - Journal article
AN - SCOPUS:84996555070
VL - 12
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 097
ER -
ID: 179093412