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We offer a complete classification of right coideal subalgebras which containall group-like elements for the multiparameter version of the quantum group$U_q(\mathfrak{sl}_{n+1})$ provided that the main parameter $q$ is not a rootof 1. As a consequence, we determine that for each subgroup $\Sigma $ of thegroup $G$ of all group-like elements the quantum Borel subalgebra $U_q^+(\mathfrak{sl}_{n+1})$ containes $(n+1)!$ different homogeneous right coidealsubalgebras $U$ such that $U\cap G=\Sigma .$ If $q$ has a finite multiplicativeorder $t>2,$ the classification remains valid for homogeneous right coidealsubalgebras of the multiparameter version of the Lusztig quantum group $u_q(\frak{sl}_{n+1}).$ In the paper we consider the quantifications of Kac-Moodyalgebras as character Hopf algebras [V.K. Kharchenko, A combinatorial approachto the quantifications of Lie algebras, Pacific J. Math., 203(1)(2002), 191-233].

Right coideal subalgebras in $U_q(\frak{sl}_{n+1}).$