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We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group provided that is not a root of 1. If has a finite multiplicative order ; this classification remains valid for homogeneous right coideal subalgebras
of the Frobenius–Lusztig kernel . In particular, the total number of right coideal
subalgebras that contain the coradical equals ; the order of the Weyl group defined by the root system of type .
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