Journal of Mathematical Physics, Analysis, Geometry 2021, vol. 17, No 4, pp. 484-508   https://doi.org/10.15407/mag17.04.484     ( to contents , go back )

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

Sergey D. Sinel'shchikov

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

This work presents a classification of $U_q(\mathfrak{sl}_2)$-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.