Abstract
We construct an action of a compact matrix quantum group on a Cuntz algebra or a UHF-algebra, and investigate the fixed point subalgebra of the algebra under the action. Especially we cnsider the action of μ U(2) on the Cuntz algebra O 2 and the action of S μ U(2) on the UHF-algebra of type 2 ∞. We show that these fixed point subalgebras are generated by a sequence of Jones' projections
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