Quantum group actions on the Cuntz algebra (Q5931558)

The authors give explicit actions of a quantised universal enveloping algebra \(U_{q}(g)\) on the Cuntz algebra \(O_{d}\) on \(d\) generators. It is shown that this action makes \(O_{d}\) a module algebra. Dually, the coaction of the quantum group of function type \(G_{q}\) corresponding to \(U_{q}(g)\) on \(O_{d}\) is described, thus making the latter a \(G_{q}\)-comodule algebra. The subalgebras of (co)invariants of \(O_{q}\) with respect to the above (co)actions are computed in the case of classical quantum algebras and groups.