Abstract
We offer a complete classification of right coideal subalgebras which contain all group-like elements for the multiparameter version of the quantum group U q ( sl n + 1 ) 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 U q + ( sl n + 1 ) 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 u q ( sl n + 1 ) . 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].
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