Uq (sl2)-Symmetries of the Quantum Disc: a Complete List

This work presents a classification of U-q (sl(2))-symmetries on the quantum disc. The principal invariant of such classification, the grading jump, is introduced. It turns out that, under the present subjects, the grading jump can take only 3 values: 0, 1, 1. The subcollection of the complete collection of symmetries is extracted in such a way that the selected symmetries satisfy certain compatibility condition for involutions.