2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153699Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of quantum mechanics is discussed.23 pages Latex, to appear in Lie goups, their representations, generalizations and applications, KluwerQuantum Algebratext