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Fixed Point Algebras for Easy Quantum Groups
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 -groups. Building on prior work by the second author, we prove that
free easy quantum groups satisfy these conditions and we compute the -groups
of their fixed point algebras in a general form. We then turn to examples such
as the quantum permutation group , the free orthogonal quantum group
and the quantum reflection groups . Our fixed point-algebra
construction provides concrete examples of free actions of free orthogonal easy
quantum groups, which are related to Hopf-Galois extensions
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