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A -algebra is called residually finite-dimensional (RFD for short) if there exists a set of representations such that is faithful.
Equivalently, is RFD if finite-dimensional representations separate its points. That is, for every , there is a finite-dimensional representation such that .
A discrete quantum group is called residually finite if is RFD.
If and are finitely generated and residually finite, then is residually finite. [BCF18]
If is residually finite, then
Quantum group is residually finite if