Right coideal subalgebras in

We offer a complete classification of right coideal subalgebras which contain all group-like elements for the multiparameter version of the quantum group provided that the main parameter q is not a root of 1. As a consequence, we determine that for each subgroup Σ of the group G of all group-like elements the quantum Borel subalgebra contains (n+1)! different homogeneous right coideal subalgebras U such that U∩G=Σ. If q has a finite multiplicative order t>2, the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the Lusztig quantum group . In the paper we consider the quantifications of Kac–Moody algebras as character Hopf algebras [V.K. Kharchenko, A combinatorial approach to the quantifications of Lie algebras, Pacific J. Math. 203 (1) (2002) 191–233].