We give a complete classification of right coideal subalgebras that contain all group-like elements for the quantum group $U_q^+(\frak{ so}_{ 2n+1}),$ provided that $q$ is not a root of 1. If $q$ has a finite multiplicative order $t>4,$ this classification remains valid for homogeneous right coideal subalgebras of the small Lusztig quantum group $u_q^+(\frak{ so}_{ 2n+1}).$ As a consequence, we determine that the total number of right coideal subalgebras that contain the coradical equals $(2n)!!,$ the order of the Weyl group defined by the root system of type $B_n.$
Categories: math.QA math.RA