Fixed point algebras for easy quantum groups
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- Gabriel_2016_Fixed_Point
Final published version, 548 KB, PDF document
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.
Original language | English |
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Article number | 097 |
Journal | Symmetry, Integrability and Geometry: Methods and Applications |
Volume | 12 |
Number of pages | 21 |
ISSN | 1815-0659 |
DOIs | |
Publication status | Published - 2016 |
- Easy quantum groups, Free actions, Free orthogonal quantum groups, Fusion rules, K-theory, Kirchberg algebras, Noncrossing partitions, Quantum permutation groups, Quantum reflection groups
Research areas
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