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

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dc.creatorKharchenko, V.
dc.creatorSagahon, A. V. Lara
dc.date2007-10-11
dc.date2008-04-12
dc.date.accessioned2026-07-07T09:31:53Z
dc.date.available2026-07-07T09:31:53Z
dc.descriptionWe offer a complete classification of right coideal subalgebras which contain all 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 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 $U_q^+ (\mathfrak{sl}_{n+1})$ containes $(n+1)!$ different homogeneous right coideal subalgebras $U$ such that $U\cap G=Σ.$ 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 $u_q (\frak{sl}_{n+1}).$ 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].
dc.identifierhttps://arxiv.org/abs/0710.2143
dc.identifierhttp://arxiv.org/abs/0710.2143
dc.identifierJournal of Algebra, 319(2008), 2571-2625
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158619
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject16W30; 17B37
dc.titleRight coideal subalgebras in $U_q(\frak{sl}_{n+1}).$
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