2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58869We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their commutative counterparts. This survey can be considered as the second part of the previous survey (J. of Lie Theory vol. 3 (1993), 149-176.48 pages, LaTeX2e, no figureQuantum AlgebraMathematical PhysicsOperator AlgebrasRepresentation Theorytext